Polar coding systems, procedures, and signaling

ABSTRACT

Systems, methods, and instrumentalities are disclosed for interleaving coded bits. A wireless transmit/receive unit (WTRU) may generate a plurality of polar encoded bits using polar encoding. The WTRU may divide the plurality of polar encoded bits into sub-blocks of equal size in a sequential manner. The WTRU may apply sub-block wise interleaving to the sub-blocks using an interleaver pattern. The sub-blocks associated with a subset of the sub-blocks may be interleaved, and sub-blocks associated with another subset of the sub-blocks may not be interleaved. The sub-block wise interleaving may include applying interleaving across the sub-blocks without interleaving bits associated with each of the sub-blocks. The WTRU may concatenate bits from each of the interleaved sub-blocks to generate interleaved bits, and store the interleaved bits associated with the interleaved sub-blocks in a circular buffer. The WTRU may select a plurality of bits for transmission from the interleaved bits.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Non-Provisional applicationSer. No. 17/350,054, filed Jun. 17, 2021, which is a continuation ofU.S. Non-Provisional application Ser. No. 16/494,666, filed Sep. 16,2019, which issued as U.S. Pat. No. 11,070,317 on Jul. 20, 2021, whichis the National Stage entry under 35 U.S.C. § 371 of Patent CooperationTreaty Application PCT/US2018/023530, filed Mar. 21, 2018, which claimsthe benefit of U.S. Provisional Patent Application Nos. 62/474,875,filed Mar. 22, 2017, 62/500,887 filed May 3, 2017, 62/519,700 filed Jun.14, 2017, 62/545,615 filed Aug. 15, 2017, and 62/556,104 filed Sep. 8,2017, the contents of which are incorporated by reference.

BACKGROUND

Mobile communications continue to evolve. A fifth generation of mobilecommunications technologies may be referred to as 5G. A 5G mobilewireless communication system may implement a variety of radio accesstechnologies (RATs), including New Radio (NR). Use cases for NR mayinclude, for example, extreme Mobile Broadband (eMBB), Ultra HighReliability and Low Latency Communications (URLLC), and massive MachineType Communications (mMTC). Existing coding schemes and processing ofencoded bits used for transmission of control information and/or datamay be supplemented by new coding schemes and processing mechanisms ofcoded bits.

SUMMARY

Systems, methods, and instrumentalities are disclosed for interleavingpolar encoded bits as part of rate matching. A wireless transmit/receiveunit (WTRU) may generate a plurality of polar encoded bits using polarencoding. The plurality of polar encoded bits may be generated using amother code length. The WTRU may divide the plurality of polar encodedbits into sub-blocks of equal size. The polar encoded bits may bedivided into sub-blocks in a sequential manner. The size of each of thesub-blocks may be a ratio of the mother code length and a number of thesub-blocks. The WTRU may apply sub-block wise interleaving to thesub-blocks using an interleaver pattern. The interleaver pattern may begiven by d₁( ) in the following equation:

${I_{s}(i)} = {{B \cdot {d_{1}\left( \frac{i}{B} \right)}} + {{d_{2}\left( {{mod}\left( {i,B} \right)} \right)}.}}$

Sub-blocks associated with a subset of the sub-blocks may beinterleaved, and sub-blocks associated with another subset of thesub-blocks may not be interleaved. The sub-block wise interleaving mayinclude applying interleaving across the sub-blocks without interleavingbits associated with each of the sub-blocks. For example, the groups ofbits or sub-blocks may be interleaved, while the bits within a sub-blockmay not be interleaved. The subset of sub-blocks that are interleavedand the subset of sub-blocks that are not interleaved may be consecutiveand non-overlapping.

The WTRU may concatenate bits from each of the interleaved sub-blocks togenerate interleaved bits. For example, the concatenated bits may beformed from the sub-blocks that are interleaved, while the bits withineach of the sub-blocks are not interleaved. The bits associated witheach of the interleaved sub-blocks may be sequentially concatenated. TheWTRU may store the interleaved bits associated with the interleavedsub-blocks in a circular buffer. The WTRU may select a plurality of bits(e.g., a contiguous plurality of bits) for transmission from theinterleaved bits. The plurality of bits may be may be contiguouslystored in the circular buffer. The plurality of bits may be selectedbased on a rate matching scheme. The rate matching scheme may bedetermined based on a mother code length, a rate matching output size,and a code rate. The rate matching scheme may be one of a repetitionscheme, a puncturing scheme, or a shortening scheme. For example, therate matching scheme may be a repetition scheme, e.g., when ratematching output size is greater than the mother code length. The ratematching scheme may be a shortening scheme or a puncturing scheme, whenrate matching output size is less than the mother code length. Selectionbetween the shortening scheme and the puncturing scheme may be based ona code rate.

A first subset of sub-blocks that are interleaved may include the middlesub-blocks of the number of sub-blocks, and wherein a second subset ofsub-blocks that are not interleaved may be an even number of sub-blocks.The second subset of sub-blocks comprises an equal number of sub-blockson each side of the first subset of sub-blocks. A third subset ofsub-blocks that is interleaved may be adjacent to the second subset ofsub-blocks. A fourth subset of sub-blocks that is not interleaved mayinclude sub-blocks other than the first subset of sub-blocks, the secondsubset of sub-blocks, and the third subset of sub-blocks. The fourthsubset of sub-blocks may be adjacent to the third subset of sub-blocks.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a system diagram illustrating an example communicationssystem in which one or more disclosed embodiments may be implemented.

FIG. 1B is a system diagram illustrating an example wirelesstransmit/receive unit (WTRU) that may be used within the communicationssystem illustrated in FIG. 1A according to an embodiment.

FIG. 1C is a system diagram illustrating an example radio access network(RAN) and an example core network (CN) that may be used within thecommunications system illustrated in FIG. 1A according to an embodiment.

FIG. 1D is a system diagram illustrating a further example RAN and afurther example CN that may be used within the communications systemillustrated in FIG. 1A according to an embodiment.

FIG. 2 illustrates an exemplary polar encoder.

FIG. 3 illustrates an exemplary polar coding.

FIG. 4 illustrates an exemplary of a parity check (PC) polar coding.

FIG. 5 illustrates an example of processing for control informationusing polar coding.

FIG. 6 illustrates an exemplary implementation of rate matching control.

FIG. 7 illustrates an exemplary rate matching.

FIG. 8 illustrates an exemplary bit selection.

FIG. 9 illustrates an exemplary bit selection.

FIG. 10 illustrates an exemplary bit selection.

FIG. 11 illustrates an exemplary bit selection.

FIG. 12 illustrates an exemplary bit selection.

FIG. 13 illustrates an exemplary encoding of cyclic redundancy check(CRC)-aided (CA) polar code with a long CRC.

FIG. 14 illustrates an exemplary distribution of decoding for CA polarcode with a long CRC.

FIG. 15 illustrates an exemplary encoding of CA polar code with twoseparate CRCs.

FIG. 16 illustrates an exemplary decoding of CA polar code with twoseparate CRCs.

FIG. 17 illustrates an exemplary encoding of PC polar code.

FIG. 18 illustrates an exemplary decoding of PC polar code.

FIG. 19 illustrates an exemplary decoding of PC polar code with CA listselection.

FIG. 20 illustrates an exemplary block error ratio (BLER) comparisonbetween sub-block based puncturing and a prior shortening scheme.

FIG. 21 illustrates an exemplary sub-block wise interleaver for polarcode rate matching with 8 sub-blocks.

FIG. 22 illustrates an exemplary sub-block wise interleaver for polarcode rate matching with 16 sub-blocks.

FIGS. 23A-23C illustrate an exemplary sub-block wise interleaver forpolar code rate matching with 32 sub-blocks.

FIG. 24 illustrates an exemplary 16 quadrature amplitude modulation(QAM) modulation.

FIG. 25 illustrates an exemplary 16QAM modulation.

FIG. 26 illustrates an exemplary 16QAM modulation with 4 partitions.

FIG. 27 illustrates an exemplary quadrature phase shift keying (QPSK)modulation with 2 partitions.

FIG. 28 illustrates an exemplary QPSK modulation with 2 partitions.

FIG. 29 illustrates an exemplary QPSK modulation with 5 partitions.

FIG. 30 illustrates an exemplary channel interleaver.

FIG. 31 illustrates an example of interleaving.

FIG. 32 illustrates an exemplary block interleaver with depth 5.

FIG. 33 illustrates an exemplary performance comparison of differentinterleavers at tapped delay line (TDL)-A channel model with delayspread 100 ns, ½ code rate, and QPSK modulation.

FIG. 34 illustrates an exemplary performance comparison of differentinterleavers at TDL-A channel model with delay spread 100 ns, ½ coderate, and 16QAM modulation.

FIG. 35 illustrates an exemplary performance comparison of differentinterleavers at TDL-A channel model with delay spread 100 ns, ½ coderate, and 64QAM modulation.

FIG. 36 illustrates an example of a performance improvement that may beseen using a row-column interleaver.

FIGS. 37-48 illustrate exemplary performance comparisons of variousexemplary methods and schemes disclosed herein.

FIG. 49 illustrates an exemplary triangular interleaver.

FIG. 50 illustrates an exemplary triangular interleaver.

FIG. 51 illustrates an exemplary polar encoding system.

DETAILED DESCRIPTION

A detailed description of illustrative examples will now be describedwith reference to the various figures. Although this descriptionprovides a detailed example of possible implementations, it should benoted that the details are intended to be exemplary and in no way limitthe scope of the application.

FIG. 1A is a diagram illustrating an example communications system 100in which one or more disclosed embodiments may be implemented. Thecommunications system 100 may be a multiple access system that providescontent, such as voice, data, video, messaging, broadcast, etc., tomultiple wireless users. The communications system 100 may enablemultiple wireless users to access such content through the sharing ofsystem resources, including wireless bandwidth. For example, thecommunications systems 100 may employ one or more channel accessmethods, such as code division multiple access (CDMA), time divisionmultiple access (TDMA), frequency division multiple access (FDMA),orthogonal FDMA (OFDMA), single-carrier FDMA (SC-FDMA), zero-tailunique-word DFT-Spread OFDM (ZT UW DTS-s OFDM), unique word OFDM(UW-OFDM), resource block-filtered OFDM, filter bank multicarrier(FBMC), and the like.

As shown in FIG. 1A, the communications system 100 may include wirelesstransmit/receive units (WTRUs) 102 a, 102 b, 102 c, 102 d, a RAN104/113, a CN 106/115, a public switched telephone network (PSTN) 108,the Internet 110, and other networks 112, though it will be appreciatedthat the disclosed embodiments contemplate any number of WTRUs, basestations, networks, and/or network elements. Each of the WTRUs 102 a,102 b, 102 c, 102 d may be any type of device configured to operateand/or communicate in a wireless environment. By way of example, theWTRUs 102 a, 102 b, 102 c, 102 d, any of which may be referred to as a“station” and/or a “STA”, may be configured to transmit and/or receivewireless signals and may include a user equipment (UE), a mobilestation, a fixed or mobile subscriber unit, a subscription-based unit, apager, a cellular telephone, a personal digital assistant (PDA), asmartphone, a laptop, a netbook, a personal computer, a wireless sensor,a hotspot or Mi-Fi device, an Internet of Things (IoT) device, a watchor other wearable, a head-mounted display (HMD), a vehicle, a drone, amedical device and applications (e.g., remote surgery), an industrialdevice and applications (e.g., a robot and/or other wireless devicesoperating in an industrial and/or an automated processing chaincontexts), a consumer electronics device, a device operating oncommercial and/or industrial wireless networks, and the like. Any of theWTRUs 102 a, 102 b, 102 c and 102 d may be interchangeably referred toas a UE.

The communications systems 100 may also include a base station 114 aand/or a base station 114 b. Each of the base stations 114 a, 114 b maybe any type of device configured to wirelessly interface with at leastone of the WTRUs 102 a, 102 b, 102 c, 102 d to facilitate access to oneor more communication networks, such as the CN 106/115, the Internet110, and/or the other networks 112. By way of example, the base stations114 a, 114 b may be a base transceiver station (BTS), a Node-B, an eNodeB, a Home Node B, a Home eNode B, a gNB, a NR NodeB, a site controller,an access point (AP), a wireless router, and the like. While the basestations 114 a, 114 b are each depicted as a single element, it will beappreciated that the base stations 114 a, 114 b may include any numberof interconnected base stations and/or network elements.

The base station 114 a may be part of the RAN 104/113, which may alsoinclude other base stations and/or network elements (not shown), such asa base station controller (BSC), a radio network controller (RNC), relaynodes, etc. The base station 114 a and/or the base station 114 b may beconfigured to transmit and/or receive wireless signals on one or morecarrier frequencies, which may be referred to as a cell (not shown).These frequencies may be in licensed spectrum, unlicensed spectrum, or acombination of licensed and unlicensed spectrum. A cell may providecoverage for a wireless service to a specific geographical area that maybe relatively fixed or that may change over time. The cell may furtherbe divided into cell sectors. For example, the cell associated with thebase station 114 a may be divided into three sectors. Thus, in oneembodiment, the base station 114 a may include three transceivers, i.e.,one for each sector of the cell. In an embodiment, the base station 114a may employ multiple-input multiple output (MIMO) technology and mayutilize multiple transceivers for each sector of the cell. For example,beamforming may be used to transmit and/or receive signals in desiredspatial directions.

The base stations 114 a, 114 b may communicate with one or more of theWTRUs 102 a, 102 b, 102 c, 102 d over an air interface 116, which may beany suitable wireless communication link (e.g., radio frequency (RF),microwave, centimeter wave, micrometer wave, infrared (IR), ultraviolet(UV), visible light, etc.). The air interface 116 may be establishedusing any suitable radio access technology (RAT).

More specifically, as noted above, the communications system 100 may bea multiple access system and may employ one or more channel accessschemes, such as CDMA, TDMA, FDMA, OFDMA, SC-FDMA, and the like. Forexample, the base station 114 a in the RAN 104/113 and the WTRUs 102 a,102 b, 102 c may implement a radio technology such as Universal MobileTelecommunications System (UMTS) Terrestrial Radio Access (UTRA), whichmay establish the air interface 115/116/117 using wideband CDMA (WCDMA).WCDMA may include communication protocols such as High-Speed PacketAccess (HSPA) and/or Evolved HSPA (HSPA+). HSPA may include High-SpeedDownlink (DL) Packet Access (HSDPA) and/or High-Speed UL Packet Access(HSUPA).

In an embodiment, the base station 114 a and the WTRUs 102 a, 102 b, 102c may implement a radio technology such as Evolved UMTS TerrestrialRadio Access (E-UTRA), which may establish the air interface 116 usingLong Term Evolution (LTE) and/or LTE-Advanced (LTE-A) and/orLTE-Advanced Pro (LTE-A Pro).

In an embodiment, the base station 114 a and the WTRUs 102 a, 102 b, 102c may implement a radio technology such as NR Radio Access, which mayestablish the air interface 116 using New Radio (NR).

In an embodiment, the base station 114 a and the WTRUs 102 a, 102 b, 102c may implement multiple radio access technologies. For example, thebase station 114 a and the WTRUs 102 a, 102 b, 102 c may implement LTEradio access and NR radio access together, for instance using dualconnectivity (DC) principles. Thus, the air interface utilized by WTRUs102 a, 102 b, 102 c may be characterized by multiple types of radioaccess technologies and/or transmissions sent to/from multiple types ofbase stations (e.g., a eNB and a gNB).

In other embodiments, the base station 114 a and the WTRUs 102 a, 102 b,102 c may implement radio technologies such as IEEE 802.11 (i.e.,Wireless Fidelity (WiFi), IEEE 802.16 (i.e., Worldwide Interoperabilityfor Microwave Access (WiMAX)), CDMA2000, CDMA2000 1×, CDMA2000 EV-DO,Interim Standard 2000 (IS-2000), Interim Standard 95 (IS-95), InterimStandard 856 (IS-856), Global System for Mobile communications (GSM),Enhanced Data rates for GSM Evolution (EDGE), GSM EDGE (GERAN), and thelike.

The base station 114 b in FIG. 1A may be a wireless router, Home Node B,Home eNode B, or access point, for example, and may utilize any suitableRAT for facilitating wireless connectivity in a localized area, such asa place of business, a home, a vehicle, a campus, an industrialfacility, an air corridor (e.g., for use by drones), a roadway, and thelike. In one embodiment, the base station 114 b and the WTRUs 102 c, 102d may implement a radio technology such as IEEE 802.11 to establish awireless local area network (WLAN). In an embodiment, the base station114 b and the WTRUs 102 c, 102 d may implement a radio technology suchas IEEE 802.15 to establish a wireless personal area network (WPAN). Inyet another embodiment, the base station 114 b and the WTRUs 102 c, 102d may utilize a cellular-based RAT (e.g., WCDMA, CDMA2000, GSM, LTE,LTE-A, LTE-A Pro, NR etc.) to establish a picocell or femtocell. Asshown in FIG. 1A, the base station 114 b may have a direct connection tothe Internet 110. Thus, the base station 114 b may not be required toaccess the Internet 110 via the CN 106/115.

The RAN 104/113 may be in communication with the CN 106/115, which maybe any type of network configured to provide voice, data, applications,and/or voice over internet protocol (VoIP) services to one or more ofthe WTRUs 102 a, 102 b, 102 c, 102 d. The data may have varying qualityof service (QoS) requirements, such as differing throughputrequirements, latency requirements, error tolerance requirements,reliability requirements, data throughput requirements, mobilityrequirements, and the like. The CN 106/115 may provide call control,billing services, mobile location-based services, pre-paid calling,Internet connectivity, video distribution, etc., and/or performhigh-level security functions, such as user authentication. Although notshown in FIG. 1A, it will be appreciated that the RAN 104/113 and/or theCN 106/115 may be in direct or indirect communication with other RANsthat employ the same RAT as the RAN 104/113 or a different RAT. Forexample, in addition to being connected to the RAN 104/113, which may beutilizing a NR radio technology, the CN 106/115 may also be incommunication with another RAN (not shown) employing a GSM, UMTS, CDMA2000, WiMAX, E-UTRA, or WiFi radio technology.

The CN 106/115 may also serve as a gateway for the WTRUs 102 a, 102 b,102 c, 102 d to access the PSTN 108, the Internet 110, and/or the othernetworks 112. The PSTN 108 may include circuit-switched telephonenetworks that provide plain old telephone service (POTS). The Internet110 may include a global system of interconnected computer networks anddevices that use common communication protocols, such as thetransmission control protocol (TCP), user datagram protocol (UDP) and/orthe internet protocol (IP) in the TCP/IP internet protocol suite. Thenetworks 112 may include wired and/or wireless communications networksowned and/or operated by other service providers. For example, thenetworks 112 may include another CN connected to one or more RANs, whichmay employ the same RAT as the RAN 104/113 or a different RAT.

Some or all of the WTRUs 102 a, 102 b, 102 c, 102 d in thecommunications system 100 may include multi-mode capabilities (e.g., theWTRUs 102 a, 102 b, 102 c, 102 d may include multiple transceivers forcommunicating with different wireless networks over different wirelesslinks). For example, the WTRU 102 c shown in FIG. 1A may be configuredto communicate with the base station 114 a, which may employ acellular-based radio technology, and with the base station 114 b, whichmay employ an IEEE 802 radio technology.

FIG. 1B is a system diagram illustrating an example WTRU 102. As shownin FIG. 1B, the WTRU 102 may include a processor 118, a transceiver 120,a transmit/receive element 122, a speaker/microphone 124, a keypad 126,a display/touchpad 128, non-removable memory 130, removable memory 132,a power source 134, a global positioning system (GPS) chipset 136,and/or other peripherals 138, among others. It will be appreciated thatthe WTRU 102 may include any sub-combination of the foregoing elementswhile remaining consistent with an embodiment.

The processor 118 may be a general purpose processor, a special purposeprocessor, a conventional processor, a digital signal processor (DSP), aplurality of microprocessors, one or more microprocessors in associationwith a DSP core, a controller, a microcontroller, Application SpecificIntegrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs)circuits, any other type of integrated circuit (IC), a state machine,and the like. The processor 118 may perform signal coding, dataprocessing, power control, input/output processing, and/or any otherfunctionality that enables the WTRU 102 to operate in a wirelessenvironment. The processor 118 may be coupled to the transceiver 120,which may be coupled to the transmit/receive element 122. While FIG. 1Bdepicts the processor 118 and the transceiver 120 as separatecomponents, it will be appreciated that the processor 118 and thetransceiver 120 may be integrated together in an electronic package orchip.

The transmit/receive element 122 may be configured to transmit signalsto, or receive signals from, a base station (e.g., the base station 114a) over the air interface 116. For example, in one embodiment, thetransmit/receive element 122 may be an antenna configured to transmitand/or receive RF signals. In an embodiment, the transmit/receiveelement 122 may be an emitter/detector configured to transmit and/orreceive IR, UV, or visible light signals, for example. In yet anotherembodiment, the transmit/receive element 122 may be configured totransmit and/or receive both RF and light signals. It will beappreciated that the transmit/receive element 122 may be configured totransmit and/or receive any combination of wireless signals.

Although the transmit/receive element 122 is depicted in FIG. 1B as asingle element, the WTRU 102 may include any number of transmit/receiveelements 122. More specifically, the WTRU 102 may employ MIMOtechnology. Thus, in one embodiment, the WTRU 102 may include two ormore transmit/receive elements 122 (e.g., multiple antennas) fortransmitting and receiving wireless signals over the air interface 116.

The transceiver 120 may be configured to modulate the signals that areto be transmitted by the transmit/receive element 122 and to demodulatethe signals that are received by the transmit/receive element 122. Asnoted above, the WTRU 102 may have multi-mode capabilities. Thus, thetransceiver 120 may include multiple transceivers for enabling the WTRU102 to communicate via multiple RATs, such as NR and IEEE 802.11, forexample.

The processor 118 of the WTRU 102 may be coupled to, and may receiveuser input data from, the speaker/microphone 124, the keypad 126, and/orthe display/touchpad 128 (e.g., a liquid crystal display (LCD) displayunit or organic light-emitting diode (OLED) display unit). The processor118 may also output user data to the speaker/microphone 124, the keypad126, and/or the display/touchpad 128. In addition, the processor 118 mayaccess information from, and store data in, any type of suitable memory,such as the non-removable memory 130 and/or the removable memory 132.The non-removable memory 130 may include random-access memory (RAM),read-only memory (ROM), a hard disk, or any other type of memory storagedevice. The removable memory 132 may include a subscriber identitymodule (SIM) card, a memory stick, a secure digital (SD) memory card,and the like. In other embodiments, the processor 118 may accessinformation from, and store data in, memory that is not physicallylocated on the WTRU 102, such as on a server or a home computer (notshown).

The processor 118 may receive power from the power source 134, and maybe configured to distribute and/or control the power to the othercomponents in the WTRU 102. The power source 134 may be any suitabledevice for powering the WTRU 102. For example, the power source 134 mayinclude one or more dry cell batteries (e.g., nickel-cadmium (NiCd),nickel-zinc (NiZn), nickel metal hydride (NiMH), lithium-ion (Li-ion),etc.), solar cells, fuel cells, and the like.

The processor 118 may also be coupled to the GPS chipset 136, which maybe configured to provide location information (e.g., longitude andlatitude) regarding the current location of the WTRU 102. In additionto, or in lieu of, the information from the GPS chipset 136, the WTRU102 may receive location information over the air interface 116 from abase station (e.g., base stations 114 a, 114 b) and/or determine itslocation based on the timing of the signals being received from two ormore nearby base stations. It will be appreciated that the WTRU 102 mayacquire location information by way of any suitablelocation-determination method while remaining consistent with anembodiment.

The processor 118 may further be coupled to other peripherals 138, whichmay include one or more software and/or hardware modules that provideadditional features, functionality and/or wired or wirelessconnectivity. For example, the peripherals 138 may include anaccelerometer, an e-compass, a satellite transceiver, a digital camera(for photographs and/or video), a universal serial bus (USB) port, avibration device, a television transceiver, a hands free headset, aBluetooth® module, a frequency modulated (FM) radio unit, a digitalmusic player, a media player, a video game player module, an Internetbrowser, a Virtual Reality and/or Augmented Reality (VR/AR) device, anactivity tracker, and the like. The peripherals 138 may include one ormore sensors, the sensors may be one or more of a gyroscope, anaccelerometer, a hall effect sensor, a magnetometer, an orientationsensor, a proximity sensor, a temperature sensor, a time sensor; ageolocation sensor; an altimeter, a light sensor, a touch sensor, amagnetometer, a barometer, a gesture sensor, a biometric sensor, and/ora humidity sensor.

The WTRU 102 may include a full duplex radio for which transmission andreception of some or all signals (e.g., associated with subframes forboth the UL (e.g., for transmission) and downlink (e.g., for reception)may be concurrent and/or simultaneous. The full duplex radio may includean interference management unit to reduce and or substantially eliminateself-interference via either hardware (e.g., a choke) or signalprocessing via a processor (e.g., a separate processor (not shown) orvia processor 118). In an embodiment, the WRTU 102 may include ahalf-duplex radio for which transmission and reception of some or all ofthe signals (e.g., associated with particular subframes for either theUL (e.g., for transmission) or the downlink (e.g., for reception)).

FIG. 1C is a system diagram illustrating the RAN 104 and the CN 106according to an embodiment. As noted above, the RAN 104 may employ anE-UTRA radio technology to communicate with the WTRUs 102 a, 102 b, 102c over the air interface 116. The RAN 104 may also be in communicationwith the CN 106.

The RAN 104 may include eNode-Bs 160 a, 160 b, 160 c, though it will beappreciated that the RAN 104 may include any number of eNode-Bs whileremaining consistent with an embodiment. The eNode-Bs 160 a, 160 b, 160c may each include one or more transceivers for communicating with theWTRUs 102 a, 102 b, 102 c over the air interface 116. In one embodiment,the eNode-Bs 160 a, 160 b, 160 c may implement MIMO technology. Thus,the eNode-B 160 a, for example, may use multiple antennas to transmitwireless signals to, and/or receive wireless signals from, the WTRU 102a.

Each of the eNode-Bs 160 a, 160 b, 160 c may be associated with aparticular cell (not shown) and may be configured to handle radioresource management decisions, handover decisions, scheduling of usersin the UL and/or DL, and the like. As shown in FIG. 1C, the eNode-Bs 160a, 160 b, 160 c may communicate with one another over an X2 interface.

The CN 106 shown in FIG. 1C may include a mobility management entity(MME) 162, a serving gateway (SGW) 164, and a packet data network (PDN)gateway (or PGW) 166. While each of the foregoing elements are depictedas part of the CN 106, it will be appreciated that any of these elementsmay be owned and/or operated by an entity other than the CN operator.

The MME 162 may be connected to each of the eNode-Bs 162 a, 162 b, 162 cin the RAN 104 via an S1 interface and may serve as a control node. Forexample, the MME 162 may be responsible for authenticating users of theWTRUs 102 a, 102 b, 102 c, bearer activation/deactivation, selecting aparticular serving gateway during an initial attach of the WTRUs 102 a,102 b, 102 c, and the like. The MME 162 may provide a control planefunction for switching between the RAN 104 and other RANs (not shown)that employ other radio technologies, such as GSM and/or WCDMA.

The SGW 164 may be connected to each of the eNode Bs 160 a, 160 b, 160 cin the RAN 104 via the S1 interface. The SGW 164 may generally route andforward user data packets to/from the WTRUs 102 a, 102 b, 102 c. The SGW164 may perform other functions, such as anchoring user planes duringinter-eNode B handovers, triggering paging when DL data is available forthe WTRUs 102 a, 102 b, 102 c, managing and storing contexts of theWTRUs 102 a, 102 b, 102 c, and the like.

The SGW 164 may be connected to the PGW 166, which may provide the WTRUs102 a, 102 b, 102 c with access to packet-switched networks, such as theInternet 110, to facilitate communications between the WTRUs 102 a, 102b, 102 c and IP-enabled devices.

The CN 106 may facilitate communications with other networks. Forexample, the CN 106 may provide the WTRUs 102 a, 102 b, 102 c withaccess to circuit-switched networks, such as the PSTN 108, to facilitatecommunications between the WTRUs 102 a, 102 b, 102 c and traditionalland-line communications devices. For example, the CN 106 may include,or may communicate with, an IP gateway (e.g., an IP multimedia subsystem(IMS) server) that serves as an interface between the CN 106 and thePSTN 108. In addition, the CN 106 may provide the WTRUs 102 a, 102 b,102 c with access to the other networks 112, which may include otherwired and/or wireless networks that are owned and/or operated by otherservice providers.

Although the WTRU is described in FIGS. 1A-1D as a wireless terminal, itis contemplated that in certain representative embodiments that such aterminal may use (e.g., temporarily or permanently) wired communicationinterfaces with the communication network.

In representative embodiments, the other network 112 may be a WLAN.

A WLAN in Infrastructure Basic Service Set (BSS) mode may have an AccessPoint (AP) for the BSS and one or more stations (STAs) associated withthe AP. The AP may have an access or an interface to a DistributionSystem (DS) or another type of wired/wireless network that carriestraffic in to and/or out of the BSS. Traffic to STAs that originatesfrom outside the BSS may arrive through the AP and may be delivered tothe STAs. Traffic originating from STAs to destinations outside the BSSmay be sent to the AP to be delivered to respective destinations.Traffic between STAs within the BSS may be sent through the AP, forexample, where the source STA may send traffic to the AP and the AP maydeliver the traffic to the destination STA. The traffic between STAswithin a BSS may be considered and/or referred to as peer-to-peertraffic. The peer-to-peer traffic may be sent between (e.g., directlybetween) the source and destination STAs with a direct link setup (DLS).In certain representative embodiments, the DLS may use an 802.11e DLS oran 802.11z tunneled DLS (TDLS). A WLAN using an Independent BSS (IBSS)mode may not have an AP, and the STAs (e.g., all of the STAs) within orusing the IBSS may communicate directly with each other. The IBSS modeof communication may sometimes be referred to herein as an “ad-hoc” modeof communication.

When using the 802.11ac infrastructure mode of operation or a similarmode of operations, the AP may transmit a beacon on a fixed channel,such as a primary channel. The primary channel may be a fixed width(e.g., 20 MHz wide bandwidth) or a dynamically set width via signaling.The primary channel may be the operating channel of the BSS and may beused by the STAs to establish a connection with the AP. In certainrepresentative embodiments, Carrier Sense Multiple Access with CollisionAvoidance (CSMA/CA) may be implemented, for example in in 802.11systems. For CSMA/CA, the STAs (e.g., every STA), including the AP, maysense the primary channel. If the primary channel is sensed/detectedand/or determined to be busy by a particular STA, the particular STA mayback off. One STA (e.g., only one station) may transmit at any giventime in a given BSS.

High Throughput (HT) STAs may use a 40 MHz wide channel forcommunication, for example, via a combination of the primary 20 MHzchannel with an adjacent or nonadjacent 20 MHz channel to form a 40 MHzwide channel.

Very High Throughput (VHT) STAs may support 20 MHz, 40 MHz, 80 MHz,and/or 160 MHz wide channels. The 40 MHz, and/or 80 MHz, channels may beformed by combining contiguous 20 MHz channels. A 160 MHz channel may beformed by combining 8 contiguous 20 MHz channels, or by combining twonon-contiguous 80 MHz channels, which may be referred to as an 80+80configuration. For the 80+80 configuration, the data, after channelencoding, may be passed through a segment parser that may divide thedata into two streams. Inverse Fast Fourier Transform (IFFT) processing,and time domain processing, may be done on each stream separately. Thestreams may be mapped on to the two 80 MHz channels, and the data may betransmitted by a transmitting STA. At the receiver of the receiving STA,the above described operation for the 80+80 configuration may bereversed, and the combined data may be sent to the Medium Access Control(MAC).

Sub 1 GHz modes of operation are supported by 802.11af and 802.11ah. Thechannel operating bandwidths, and carriers, are reduced in 802.11af and802.11ah relative to those used in 802.11n, and 802.11ac. 802.11afsupports 5 MHz, 10 MHz and 20 MHz bandwidths in the TV White Space(TVWS) spectrum, and 802.11ah supports 1 MHz, 2 MHz, 4 MHz, 8 MHz, and16 MHz bandwidths using non-TVWS spectrum. According to a representativeembodiment, 802.11ah may support Meter Type Control/Machine-TypeCommunications, such as MTC devices in a macro coverage area. MTCdevices may have certain capabilities, for example, limited capabilitiesincluding support for (e.g., only support for) certain and/or limitedbandwidths. The MTC devices may include a battery with a battery lifeabove a threshold (e.g., to maintain a very long battery life).

WLAN systems, which may support multiple channels, and channelbandwidths, such as 802.11n, 802.11ac, 802.11af, and 802.11ah, include achannel which may be designated as the primary channel. The primarychannel may have a bandwidth equal to the largest common operatingbandwidth supported by all STAs in the BSS. The bandwidth of the primarychannel may be set and/or limited by a STA, from among all STAs inoperating in a BSS, which supports the smallest bandwidth operatingmode. In the example of 802.11ah, the primary channel may be 1 MHz widefor STAs (e.g., MTC type devices) that support (e.g., only support) a 1MHz mode, even if the AP, and other STAs in the BSS support 2 MHz, 4MHz, 8 MHz, 16 MHz, and/or other channel bandwidth operating modes.Carrier sensing and/or Network Allocation Vector (NAV) settings maydepend on the status of the primary channel. If the primary channel isbusy, for example, due to a STA (which supports only a 1 MHz operatingmode), transmitting to the AP, the entire available frequency bands maybe considered busy even though a majority of the frequency bands remainsidle and may be available.

In the United States, the available frequency bands, which may be usedby 802.11ah, are from 902 MHz to 928 MHz. In Korea, the availablefrequency bands are from 917.5 MHz to 923.5 MHz. In Japan, the availablefrequency bands are from 916.5 MHz to 927.5 MHz. The total bandwidthavailable for 802.11ah is 6 MHz to 26 MHz depending on the country code.

FIG. 1D is a system diagram illustrating the RAN 113 and the CN 115according to an embodiment. As noted above, the RAN 113 may employ an NRradio technology to communicate with the WTRUs 102 a, 102 b, 102 c overthe air interface 116. The RAN 113 may also be in communication with theCN 115.

The RAN 113 may include gNBs 180 a, 180 b, 180 c, though it will beappreciated that the RAN 113 may include any number of gNBs whileremaining consistent with an embodiment. The gNBs 180 a, 180 b, 180 cmay each include one or more transceivers for communicating with theWTRUs 102 a, 102 b, 102 c over the air interface 116. In one embodiment,the gNBs 180 a, 180 b, 180 c may implement MIMO technology. For example,gNBs 180 a, 108 b may utilize beamforming to transmit signals to and/orreceive signals from the gNBs 180 a, 180 b, 180 c. Thus, the gNB 180 a,for example, may use multiple antennas to transmit wireless signals to,and/or receive wireless signals from, the WTRU 102 a. In an embodiment,the gNBs 180 a, 180 b, 180 c may implement carrier aggregationtechnology. For example, the gNB 180 a may transmit multiple componentcarriers to the WTRU 102 a (not shown). A subset of these componentcarriers may be on unlicensed spectrum while the remaining componentcarriers may be on licensed spectrum. In an embodiment, the gNBs 180 a,180 b, 180 c may implement Coordinated Multi-Point (CoMP) technology.For example, WTRU 102 a may receive coordinated transmissions from gNB180 a and gNB 180 b (and/or gNB 180 c).

The WTRUs 102 a, 102 b, 102 c may communicate with gNBs 180 a, 180 b,180 c using transmissions associated with a scalable numerology. Forexample, the OFDM symbol spacing and/or OFDM subcarrier spacing may varyfor different transmissions, different cells, and/or different portionsof the wireless transmission spectrum. The WTRUs 102 a, 102 b, 102 c maycommunicate with gNBs 180 a, 180 b, 180 c using subframe or transmissiontime intervals (TTIs) of various or scalable lengths (e.g., containingvarying number of OFDM symbols and/or lasting varying lengths ofabsolute time).

The gNBs 180 a, 180 b, 180 c may be configured to communicate with theWTRUs 102 a, 102 b, 102 c in a standalone configuration and/or anon-standalone configuration. In the standalone configuration, WTRUs 102a, 102 b, 102 c may communicate with gNBs 180 a, 180 b, 180 c withoutalso accessing other RANs (e.g., such as eNode-Bs 160 a, 160 b, 160 c).In the standalone configuration, WTRUs 102 a, 102 b, 102 c may utilizeone or more of gNBs 180 a, 180 b, 180 c as a mobility anchor point. Inthe standalone configuration, WTRUs 102 a, 102 b, 102 c may communicatewith gNBs 180 a, 180 b, 180 c using signals in an unlicensed band. In anon-standalone configuration WTRUs 102 a, 102 b, 102 c may communicatewith/connect to gNBs 180 a, 180 b, 180 c while also communicatingwith/connecting to another RAN such as eNode-Bs 160 a, 160 b, 160 c. Forexample, WTRUs 102 a, 102 b, 102 c may implement DC principles tocommunicate with one or more gNBs 180 a, 180 b, 180 c and one or moreeNode-Bs 160 a, 160 b, 160 c substantially simultaneously. In thenon-standalone configuration, eNode-Bs 160 a, 160 b, 160 c may serve asa mobility anchor for WTRUs 102 a, 102 b, 102 c and gNBs 180 a, 180 b,180 c may provide additional coverage and/or throughput for servicingWTRUs 102 a, 102 b, 102 c.

Each of the gNBs 180 a, 180 b, 180 c may be associated with a particularcell (not shown) and may be configured to handle radio resourcemanagement decisions, handover decisions, scheduling of users in the ULand/or DL, support of network slicing, dual connectivity, interworkingbetween NR and E-UTRA, routing of user plane data towards User PlaneFunction (UPF) 184 a, 184 b, routing of control plane informationtowards Access and Mobility Management Function (AMF) 182 a, 182 b andthe like. As shown in FIG. 1D, the gNBs 180 a, 180 b, 180 c maycommunicate with one another over an Xn interface.

The CN 115 shown in FIG. 1D may include at least one AMF 182 a, 182 b,at least one UPF 184 a, 184 b, at least one Session Management Function(SMF) 183 a, 183 b, and possibly a Data Network (DN) 185 a, 185 b. Whileeach of the foregoing elements are depicted as part of the CN 115, itwill be appreciated that any of these elements may be owned and/oroperated by an entity other than the CN operator.

The AMF 182 a, 182 b may be connected to one or more of the gNBs 180 a,180 b, 180 c in the RAN 113 via an N2 interface and may serve as acontrol node. For example, the AMF 182 a, 182 b may be responsible forauthenticating users of the WTRUs 102 a, 102 b, 102 c, support fornetwork slicing (e.g., handling of different PDU sessions with differentrequirements), selecting a particular SMF 183 a, 183 b, management ofthe registration area, termination of NAS signaling, mobilitymanagement, and the like. Network slicing may be used by the AMF 182 a,182 b in order to customize CN support for WTRUs 102 a, 102 b, 102 cbased on the types of services being utilized WTRUs 102 a, 102 b, 102 c.For example, different network slices may be established for differentuse cases such as services relying on ultra-reliable low latency (URLLC)access, services relying on enhanced massive mobile broadband (eMBB)access, services for machine type communication (MTC) access, and/or thelike. The AMF 162 may provide a control plane function for switchingbetween the RAN 113 and other RANs (not shown) that employ other radiotechnologies, such as LTE, LTE-A, LTE-A Pro, and/or non-3GPP accesstechnologies such as WiFi.

The SMF 183 a, 183 b may be connected to an AMF 182 a, 182 b in the CN115 via an N11 interface. The SMF 183 a, 183 b may also be connected toa UPF 184 a, 184 b in the CN 115 via an N4 interface. The SMF 183 a, 183b may select and control the UPF 184 a, 184 b and configure the routingof traffic through the UPF 184 a, 184 b. The SMF 183 a, 183 b mayperform other functions, such as managing and allocating UE IP address,managing PDU sessions, controlling policy enforcement and QoS, providingdownlink data notifications, and the like. A PDU session type may beIP-based, non-IP based, Ethernet-based, and the like.

The UPF 184 a, 184 b may be connected to one or more of the gNBs 180 a,180 b, 180 c in the RAN 113 via an N3 interface, which may provide theWTRUs 102 a, 102 b, 102 c with access to packet-switched networks, suchas the Internet 110, to facilitate communications between the WTRUs 102a, 102 b, 102 c and IP-enabled devices. The UPF 184, 184 b may performother functions, such as routing and forwarding packets, enforcing userplane policies, supporting multi-homed PDU sessions, handling user planeQoS, buffering downlink packets, providing mobility anchoring, and thelike.

The CN 115 may facilitate communications with other networks. Forexample, the CN 115 may include, or may communicate with, an IP gateway(e.g., an IP multimedia subsystem (IMS) server) that serves as aninterface between the CN 115 and the PSTN 108. In addition, the CN 115may provide the WTRUs 102 a, 102 b, 102 c with access to the othernetworks 112, which may include other wired and/or wireless networksthat are owned and/or operated by other service providers. In oneembodiment, the WTRUs 102 a, 102 b, 102 c may be connected to a localData Network (DN) 185 a, 185 b through the UPF 184 a, 184 b via the N3interface to the UPF 184 a, 184 b and an N6 interface between the UPF184 a, 184 b and the DN 185 a, 185 b.

In view of FIGS. 1A-1D, and the corresponding description of FIGS.1A-1D, one or more, or all, of the functions described herein withregard to one or more of: WTRU 102 a-d, Base Station 114 a-b, eNode-B160 a-c, MME 162, SGW 164, PGW 166, gNB 180 a-c, AMF 182 a-b, UPF 184a-b, SMF 183 a-b, DN 185 a-b, and/or any other device(s) describedherein, may be performed by one or more emulation devices (not shown).The emulation devices may be one or more devices configured to emulateone or more, or all, of the functions described herein. For example, theemulation devices may be used to test other devices and/or to simulatenetwork and/or WTRU functions.

The emulation devices may be designed to implement one or more tests ofother devices in a lab environment and/or in an operator networkenvironment. For example, the one or more emulation devices may performthe one or more, or all, functions while being fully or partiallyimplemented and/or deployed as part of a wired and/or wirelesscommunication network in order to test other devices within thecommunication network. The one or more emulation devices may perform theone or more, or all, functions while being temporarilyimplemented/deployed as part of a wired and/or wireless communicationnetwork. The emulation device may be directly coupled to another devicefor purposes of testing and/or may performing testing using over-the-airwireless communications.

The one or more emulation devices may perform the one or more, includingall, functions while not being implemented/deployed as part of a wiredand/or wireless communication network. For example, the emulationdevices may be utilized in a testing scenario in a testing laboratoryand/or a non-deployed (e.g., testing) wired and/or wirelesscommunication network in order to implement testing of one or morecomponents. The one or more emulation devices may be test equipment.Direct RF coupling and/or wireless communications via RF circuitry(e.g., which may include one or more antennas) may be used by theemulation devices to transmit and/or receive data.

One or more of the features disclosed herein may be implemented usingone or more of the devices, methods, and/or systems described in FIGS.1A-1D.

Capacity achieving codes other than Turbo codes and/or low-densityparity check (LDPC) codes may include polar codes. Polar codes may belinear block codes with attributes including one or more of thefollowing: low encoding and/or decoding complexity, a low error floor(e.g., very low error floor), or explicit construction schemes.

Polar code (N, K) may be based on an information block length K, and acoded block length N. The value N may be set as a power of 2, e.g.,N=2^(n) for an integer n. The generator matrix of a polar code may beexpressed by G_(N)=B_(N)F^(⊗n), where B_(N) is the bit-reversalpermutation matrix, (.)^(⊗n) denotes the n-th Kronecker power and

$F = {\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}.}$In example implementations of polar codes, the bit-reversal permutationmatrix B_(N) may be ignored at the encoder side for simplicity and thebit-reversal operation may be performed at the decoder side. FIG. 2 isan example of polar encoder with N=8. FIG. 2 shows an exampleimplementation of F®³. The codeword of polar code may be given by x₁^(N)=u₁ ^(N)G_(N).

With respect to decoding of polar encoded bits, successive cancellation(SC) decoding may be used. Advanced decoding schemes may also be usedbased on SC decoding, e.g., successive cancellation list (SCL) decodingor CRC-Aided SCL (CA-SCL) decoding.

A CRC-Aided (CA) polar code may be a polar code with CRC-AidedSuccessive Cancellation List (SCL) decoder. In CRC-aided decoding, theCRC bits may be used to select the final codeword from a list ofcandidate codewords. The final codeword may be selected at the end ofthe decoding. The CRC bits may be designed and used for error correctionpurpose, e.g., instead of error detection purpose. The CRC bits may beused for partial error detection.

Code construction(s) for polar codes may be provided. Polar codes may bestructured in terms of encoding and decoding. The design of a polar codemay depend on the mapping of the K information bits to the N input bitsof the polar encoder u₁ ^(N). The K information bits may be put on K bitchannels, e.g., the K best bit channels. The remaining N−K input bitsthat are not mapped to the information bits may be called frozen bits.The frozen bits may have a fixed value, e.g., the frozen bits may be setto a value 0. The set of the positions for frozen bits may be calledfrozen set

. The decision on the best bit channels may vary, and may depend on thechannel conditions. In determining the set of frozen channels, the bitchannels may be ranked based on their reliabilities. The reliable bitchannels may be categorized as good bit channels and the less reliablebit channels may be categorized as bad bit channels.

The reliability of a bit channel may be calculated. For instance, one ormore of the following may be used to calculate the reliabilities of bitchannels: the Bhattacharyya bounds, the Monte-Carlo estimation, the fulltransition probability matrices estimation, or the Gaussianapproximation. These schemes may have different computation complexityand may apply to different channel conditions. A parameter designsignal-to noise ratio (SNR) may be selected. For example, a design SNRmay be selected before performing the calculation of reliabilities.

The rank of a bit channel may be calculated. The rank of a bit channelmay be calculated without using the design SNR parameter. For example,the rank sequence generated from a formula or expanded from a smallsequence. Once the rank of the bit channels is determined, theinformation bits may be mapped to bit channels with high reliability.The frozen bits may be mapped to the bit channels with low reliability,as illustrated in FIG. 3 .

FIG. 4 illustrates an exemplary parity check (PC) polar coding. Adifference between a PC-polar code and a non-PC polar code may beselection of a subset of a frozen sub-channel as PC-frozen sub-channels.A PC function may be established for error correction over sub-channels.In an example (e.g., at each parity check sub-channel position), each ofthe decoded bits involved in a PC function over a PC-frozen sub-channelmay help prune a list decoding tree. In an example, paths that meet aPC-function may survive; the rest may be eliminated on the fly. A PCfunction may be established as forward-only, for example, to beconsistent with a successive cancellation-based decoder. FIG. 4illustrates an example of mapping information bits to the inputs of thePC polar code.

The introduction of the PC polar code may allow removal of the CRC bitsof CA polar codes. The PC polar code may be used for error correctionpurpose in CRC-aided Successive Cancellation List (SCL) decoding. Thismay reduce the overhead of polar code, and may result in more codinggains.

Polar codes may be used as channel codes for uplink (UL) and/or downlink(DL) control information. The CRC bits may be used for a control messageto reduce a false alarm rate. Polar codes for physical channels maysupport one of CRC+basic polar codes or J bits error detectionCRC+concatenated polar codes. The CRC+basic polar codes (e.g., CA polar)may be used with longer CRC, e.g., (J+J′) bits CRC and/or distributedCRC, e.g., J bits CRC. Concatenated polar codes may be one or more ofthe following: J′ bits CRC+basic polar, J′ bits distributed CRC+basicpolar, PC polar, or hashed sequence PC polar. A coding scheme may beimplemented that may achieve benefit(s) of both mechanisms.

A polar coding design for control and/or data information may beprovided. Unlike tail-biting convolutional code (TBCC), polar code,which is a block code, may have a fixed block length. Rate matching forpolar code may be designed to improve performance. A rate matchingselection may be performed using one or more of repetition, puncturing,and/or shortening mechanisms. Selection of the rate matching mechanismmay be performed based on one or more parameters as described herein.

Polar code designs may include a code construction selection (e.g.,CRC-aided (CA) polar coding or parity check (PC) polar coding) and/or acode sequence selection. A flexible polar coding scheme that supportsmultiple polar codes may be provided.

Polar encoding for control channels may be provided. FIG. 5 illustratesan exemplary processing of control information (e.g., downlink controlinformation (DCI) or uplink control information (UCI)), using polarcodes. Control blocks in the polar encoding sub-system may include acode selection control block and a rate matching control block.

The code selection control block may determine the type of polar code touse. The code selection control block may determine the associated CRClength. Example polar code types may include the polar code typesdescribed herein and/or their variations such as advanced PC polar codewith CA list selection. A determination of the polar code types may bebased on one or more of a WTRU category, a WTRU capability, orconfigurations. In examples, a WTRU category may correspond to a polarcode. In examples, the polar code type may be configured via a radioresource control (RRC) connection establishment message or an RRCconnection reconfiguration message. In examples, the polar code type maybe pre-defined. The corresponding CRC length may be determined. Forexample, the CRC length may be determined based on the determined polarcode type. For example, for PC polar code, a 16-bits CRC may be used;for CA polar code with a long CRC, a 19-bits CRC may be used, forexample, if the length of the list is equal to 8. The code selectioncontrol block may send the CRC length information to the CRC attachmentblock. The CRC attachment block may pass the polar code type to thechannel coding block.

The rate matching control block of FIG. 5 may perform one or more of thefollowing: calculate the desired codeword length (e.g., the number ofcoded bits for transmission) as

${\frac{K + J}{R}{bits}};$calculate the mother code length N (e.g., after calculating the desiredcodeword length); determine the rate matching scheme(s) to be used; ordetermine the detailed rate matching scheme(s). The rate matchingcontrol block may perform the calculation or make the determinationbased on one or more of the following uplink control information (UCI)or downlink control information (DCI) block size K, CRC length J, orcode rate R.

In an example, for calculating the mother code length N, the mother codelength N may be assumed to be a power of 2 due to the polar code nature.The mother code length N may be greater or smaller than the desiredcodeword length

$\frac{K + J}{R}.$For example, if the desired codeword length is slightly larger than2^(n) bits, for some integer n, then the mother code length may be2^(n), rather than 2^(n+1). The selection of mother code length may bebased on one or more formulas. In an example,

$\begin{matrix}{{N = 2^{n}},} & {{{{if}2^{n}} \leq \frac{K + J}{R} \leq {2^{n}\left( {1 + \tau} \right)}};} \\{{N = 2^{n + 1}},} & {{{if}2^{n}\left( {1 + \tau} \right)} < \frac{K + J}{R} \leq 2^{n + 1}}\end{matrix},$for some constant fraction number τ, say ⅛.

In an example,

$\begin{matrix}{{N = 2^{n}},} & {{{{if}2^{n}} \leq \frac{K + J}{R} \leq {2^{n} + \tau}};} \\{{N = 2^{n + 1}},} & {{{{if}2^{n}} + \tau} < \frac{K + J}{R} \leq 2^{n + 1}}\end{matrix},$for some constant integer τ, such as 10. Other example formulas may besimilar as above, with the value τ being a function of n. For example,for n≤5, τ=0; else τ=9/8·2^(n), and for n≤6, τ=0; else τ=9/8·2^(n). Themother code length formulas may or may not depend on code rate. Theformula and its parameter τ may be different for different code rates orcode rate ranges.

The selection of mother code length may be based on one or more look-uptables. Table 1 illustrates an example of a look-up table (LUT) forselecting a the desired codeword length for a corresponding mother codelength N. The first row of Table 1 represents a range of desiredcodeword length, and the second row represents the corresponding mothercode length. For example, if the desired codeword length is 50 bits,which is in the range of [33, 70], the mother code length may beselected as 64 bits. If the desired codeword length is 275 bits, whichis in the range of [141, 280], the selected mother code length may be256 bits. In exemplary Table 1, the maximum mother code length is fixedas 1024 bits.

TABLE 1 $\frac{K + J}{R}$ [20, 32] [33, 70] [71, 140] [141, 280] [281,550] >550 N 32 64 128 256 512 1024

Table 2 illustrates another example of a LUT where the maximum mothercode length may be of 512 bits.

TABLE 2 $\frac{K + J}{R}$ [20, 32] [33, 70] [71, 140] [141, 280] >281 N32 64 128 256 512

A determination of a mother code length may depend on a code rate. In anexample, where a coding rate may be high (e.g., >½), a desired codewordlength may be small (or slightly larger than) a length of informationbits. A mother code length may be selected to be relatively larger sothat use of such mother code length may include more information thanwhat may be included, for example, at rate=1/2.

The exemplary Table 1 and Table 2 may be applicable to certain coderates, for example, when a mother code length depends on a code rate.For example, if a code rate is larger than a threshold (e.g., ½), amother code length N may be a power of 2. The mother code length may begreater than a desired codeword length. If a code rate is less than athreshold, a mother code length N may be determined based on one or morelook-up tables, such as the Table 1 and/or Table 2. IA mother codelength selection may depend on a modulation order. For example, Table 1and Table 2 might be used for low order modulations (e.g., QPSK). Adifferent set of tables might be defined for high order modulations(e.g., 64 QAM).

FIG. 37 , FIG. 38 , FIG. 39 , and FIG. 40 illustrate a minimum SNR thatmay be needed to achieve a target BLER level of 10⁻³ for code rates ⅕,⅓, ⅖ and ½, respectively. These exemplary simulation results illustratethat where a code rate may be less than or equal to ⅖ and a coded blocklength may be between 2^(n) and 2^(n) (1+⅛), a repetition scheme may beselected. For example, if

$\frac{K + J}{R}$is between 2^(n) and 2^(n) (1+⅛) and a code rate is less than ⅖, then amother code length N may be selected as 2^(n), e.g., rather than2^(n+1).

Other performance simulations of a split-natural puncturing example, asplit-natural shortening example, and a bit-reversal shortening examplemay provide results as set forth herein. In such simulations, QPSKmodulation and AWGN channel may be assumed. In such simulations, a polarcode with PW sequence and a CA-SCL (L=8) decoding algorithm may be used.A 19-bit CRC may be appended to source data. Such CRC bits may beconsidered as part of the information bits.

The rate matching control block may determine the rate matching schemethat may be used. Rate matching schemes may include one or more of thefollowing: repetition, shortening, or puncturing. Selection of a ratematching scheme of repetition may depend on the relation between themother code length and the desired codeword length. For example, if themother code length is smaller than the desired codeword length, therepetition scheme may be selected. Otherwise, the shortening scheme orthe puncturing scheme may be selected. The selection between shorteningscheme and puncturing scheme may depend on at least one of the coderate, R or the mother code rate,

${R_{m} = \frac{K}{N}}.$Puncturing schemes may perform well, and therefore may be used, at a lowcode rate or a low mother code rate. Shortening schemes may performwell, and therefore may be used, at a high code rate or a high mothercode rate. A function of ƒ(R_(m), R) may be used. If ƒ(R_(m), R)<Thr,then puncturing scheme may be selected, otherwise, shortening scheme maybe selected.

FIG. 41 and FIG. 42 illustrate a minimum SNR that may be used to achievea target BLER level of 10⁻² and 10⁻³ respectively for a code rate 1/5.FIG. 43 and FIG. 44 , respectively, illustrate a minimum SNR that may beused to achieve a target BLER level of 10⁻² and 10⁻³ for a code rate1/3. FIG. 45 and FIG. 46 , respectively, illustrate a minimum SNR thatmay be used to achieve a target BLER level of 10⁻² and 10⁻³ for a coderate 2/5. FIG. 47 and FIG. 48 , respectively, illustrate a minimum SNRthat may be used to achieve a target BLER level of 10⁻² and 10⁻³ for acode rate 1/2.

Based on these simulation results, it may be established that where acode rate is greater than ⅖, a shortening scheme may be selected. Wherea code rate is less than or equal to ⅖, a puncturing scheme may beselected. In an example, a code rate threshold for selecting apuncturing scheme or a shortening scheme may be ⅖.

Rate matching may be implemented using concatenated polar codes (e.g.,in addition to repetition, shortening, and/or puncturing schemes). Forexample, for a desired codeword length of 288 bits, 224 bits may bepunctured or shortened from a mother code length of 512 bits. One waymay be to repeat 32 bits from a mother code length of 256 bits. Anotherway may be to partition the 288 bits to 256 bits and 32 bits. A polarcode may be used with mother code length of 256 bits and another polarcode with mother code length of 32 bits. This scheme may be used if thedesired codeword length is close to a summation of a few numbers whichare powers of 2. The repetition, shortening, or puncturing schemes maybe applied to each component of a concatenated polar code.

FIG. 6 illustrates an exemplary rate matching control processing. Indetermining a detailed rate matching scheme(s), one or more of thefollowing may apply.

If a repetition scheme is selected as a rate matching scheme, the ratematching control block of FIG. 5 may select a detailed repetitionscheme. The repetition schemes may include one or more of the following:repeat from top of circular buffer (e.g., natural repetition), repeatfrom bottom of circular buffer, repeat from top of circular buffer withbit reversal, repeat from bottom of circular buffer with bit reversal,random pick, uniformly/distributed repeat, repeat from the configuredstarting point in a continuous fashion, or repeat from the configuredstarting point in an interleaving fashion. Assuming e₀, . . . , e_(N-1)to be the polar encoded bits, and N+L to be the number of transmittedbits. The transmitted bits for repeat from top of circular buffer may berepresented as: e₀, . . . , e_(N-1), e₀, . . . , e_(L-1). Thetransmitted bits for repeat from bottom of circular buffer may berepresented as: e_(N-1), . . . , e₀, e_(N-1), . . . , e_(N-L). Thetransmitted bits for repeat from top of circular buffer with bitreversal may be represented as: e_(BR(0)), . . . , e_(BR(N-1)),e_(BR(0)), . . . , e_(BR(L-1)). The transmitted bits for repeat frombottom of circular buffer with bit reversal may be represented as:e_(BR(N-1)), . . . , e_(BR(0)), e_(BR(N-1)), . . . , e_(BR(N-L)). Aselection of a repetition scheme may depend on one or more of thefollowing: the number of repetition bits, the mother code length, or thecode rate. Based on the determined repetition scheme, a repetitionvector may be calculated. The repetition vector length may be equal tothe desired codeword length

$\frac{K + J}{R}$minus the mother code length N, where each value of the repetitionvector is an index with values between 1 and N (or between 0 and N−1).Based on the desired codeword length and the mother code length, therate matching block may determine the N output bits of a polar encoderthat may be repeated. For example, for the case of N=256,

${\frac{K + J}{R} = 260},$a repetition vector may be (1, 2, 3, 4), which may imply that the first4 bits of the polar encoder output are repeated. As illustrated in FIG.6 , the repetition vector may be sent to a rate matching block of FIG. 5.

If a puncturing scheme is selected, the rate matching block may selectthe detailed puncturing scheme. The puncturing schemes may include oneor more of the following: puncturing from top of circular buffer,puncturing from bottom of circular buffer, puncturing from top ofcircular buffer with bit reversal, puncturing from bottom of circularbuffer with bit reversal, distributed puncturing (e.g., split naturalpuncturing), puncturing from the configured starting point in acontinuous fashion, or puncturing from the configured starting point inan interleaving fashion. Assuming e₀, . . . , e_(N-1) to be the polarencoded bits, L be the number of punctured bits. The punctured bits forpuncturing from top of circular buffer may be represented as: e₀, . . ., e_(L-1). The punctured bits for puncturing from bottom of circularbuffer may be represented as: e_(N-L), . . . , e_(N-1). The puncturedbits for puncturing from top of circular buffer with bit reversal may berepresented as: e_(BR(0)), . . . , e_(BR(L-1)). The punctured bits forpuncturing from bottom of circular buffer with bit reversal may berepresented as: e_(BR(N-L)), . . . e_(BR(N-1)). The distributedpuncturing may be from 0, N/4, and/or N/2. The puncturing may beperformed sequentially. A selection of a puncturing scheme may depend onone or more of the following: the number of punctured bits, the mothercode length, the code rate, etc. Based on the selected puncturing schemeand the number of bits to be punctured, a puncturing vector may becalculated. As illustrated in FIG. 6 , the puncturing vector may be sentto a rate matching block.

Where a shortening scheme is selected, the rate matching block mayselect the detailed shortening scheme. The shortening schemes mayinclude one or more of the following: shortening from bottom of circularbuffer, shortening from bottom of circular buffer with bit reversal(e.g., referred to as bit reversal shortening), or split naturalshortening. The selection of the shortening scheme may depend on one ormore of the following: the number of punctured bits, the mother codelength, the code rate, etc. Based on a selected shortening scheme and anumber of bits to be shortened, a puncturing vector may be calculatedthat may be sent to the rate matching block. A shortening vector may becalculated that may correspond to the puncturing vector. For a polarencoder without bit reversal operations, the shortening vector may beequal to the puncturing vector. For a polar encoder with bit reversaloperations, the shortening vector may be equal to the bit reversal ofthe puncturing vector. The shortening vector may be sent to a zeroinsertion sub-block in the channel coding block.

In an example, K bits source information of downlink control information(DCI) or uplink control information (UCI) may be passed through a CRCattachment block. The length J of CRC bits may be determined by the codeselection control block of FIG. 5 . This block may support possible CRCcases, a single long CRC, two separate CRCs, a normal CRC, etc. Adifference of a CA polar encoding process with a single CRC (asillustrated in FIG. 13 ), and a PC polar encoding process (asillustrated in FIG. 17 ) may be a CRC length. A CRC may be set as J+J′for CA polar codes and as J for PC polar codes.

Source bits (e.g., after CRC is attached to the source bits) may be sentto a channel coding block of FIG. 5 . The channel coding block mayperform the polar encoding operation(s). As illustrated in FIG. 5 , thechannel coding block may include one or more of the followingsub-blocks: a zero insertion sub-block, a bit channel mapping sub-block,a sequence generation or selection sub-block, or a polar encodingsub-block. The zero insertion sub-block may insert zeros to the sequenceof (K+J) (combined source and CRC bits). The positions to insert zerosmay depend on the shortening vector input from rate matching controlblock. The sequence generation or selection sub-block may generate aranked sequence (or selects from a list of pre-generated rankedsequence), e.g., based on one or more of the given mother code length Ninput from the rate matching control block, the code type input from thecode Selection Control block, and/or as well as other factors likechannel conditions (e.g., SNR). For example, for a CA polar code withmother code length 64 and SNR of 5 dB, we may select or generate aranked sequence, or select a ranked sequence from a list ofpre-generated sequences. The bit mapping sub-block may map theinformation and/or CRC bits to the proper bit channels for a polar code.This operation may depend on the code type and input ranked sequence.For example, for PC polar code, the bit mapping sub-block may determinethe information set, PC frozen set, and/or frozen set, e.g., based onthe given ranked sequence. For CA polar code, the bit mapping sub-blockmay determine the information set and frozen set, e.g., based on thegiven ranked sequence. The bit mapping sub-block may embed a WTRU IDwith CRC bits using an operation, for example, an XOR operation. WTRU IDmay be embedded by XORing WTRU ID with PC frozen bits for PC polar code.In an example, WTRU ID may be included in a frozen set. In polar coding,the frozen set may correspond to a number of constant bits (e.g., 0). Inthis case, the constant bits may be replaced by the WTRU ID. Theinsertion of the WTRU ID in frozen set may lead to the undesired UEs tohave decoding errors. The polar encoding sub-block may perform the polarencoding operations (e.g., regular polar encoding operations), such asthe generator matrix of G_(N)=B_(N)F^(⊗n) or G_(N)=F^(⊗n).

As illustrated in FIG. 5 , the polar encoded bits may be sent to a ratematching block. The rate matching block may perform the puncturing orrepetition operations. A selection of the puncturing vector or therepetition vector may be received from the rate matching control block.FIG. 7 illustrates an example of rate matching for polar coded bits. Asillustrated in FIG. 7 , N=2^(n) bits from a polar encoding block (notshown in the FIG) may be sent to an interleaver sub-block of a ratematching block. The interleaver sub-block in an example may re-order thesub-blocks and the N polar encoded bits contained therein. Operations ofan interleaver sub-block may be associated with the rate matching schemethat may be used. In an example, if a puncturing from top of circularbuffer and/or a puncturing from bottom of circular buffer scheme isused, the interleaver sub-block may be transparent, i.e., such that aspecific operation may not be needed. In an example, if a puncturingfrom top with bit reversal and/or a puncturing from bottom of circularbuffer with bit reversal scheme is used, the interleaver sub-block mayperform bit reversal operations on the N coded bits. In an example, if adistributed puncturing scheme is used, the interleaver sub-block mayperform interlacing operations on the middle of the N coded bits.Similar operations may be used with one or more shortening schemesand/or repetition schemes.

Interleaved bits may be saved to a circular buffer or a virtual circularbuffer. As illustrated in FIG. 7 , the operation of saving bits to acircular buffer may be performed by a bit collection sub-block. Asfurther illustrated in FIG. 7 , depending on a puncturing vector or arepetition vector that may be generated by a rate matching controlblock, the bit selection sub-block may select bits from the circularbuffer. A puncturing vector or a repetition vector may be interpreted todetermine a pair of parameters (e.g., a starting point, a duration)associated with a circular buffer.

In an example, where a puncturing from top of circular buffer scheme maybe applied, where a puncturing vector may be (0, . . . , 0, 1, 1, . . ., 1), and where the first L bits are 0's and the last N−L bits are 1's,a pair of parameters may be determined (e.g., L+1, N−L). An exemplarybit selection is illustrated in FIG. 8 . As illustrated in FIG. 8 , thebits to be used may begin at an L+1 position of a circular buffer, witha bit sequence length that may be N−L. A similar operation may beapplied to a puncturing from top of circular buffer with bit reversalscheme. In such a scheme, bits may be saved to a circular buffer afterbit reversal operations. A similar operation may be applied to adistributed puncturing scheme. In such a scheme, bits may be saved to acircular buffer after interlacing or interleaving operations on themiddle of N coded bits.

In an example, where a puncturing from bottom of circular buffer schememay be applied, where a puncturing vector may be (1, . . . , 1, 0, . . ., 0), and where the first L bits are 1's and the last N−L bits are 0's,a pair of parameters (e.g., 1, L) may be determined. An exemplary bitselection is illustrated in FIG. 9 . As illustrated in FIG. 9 , bits tobe used may start at a first position of a circular buffer, with the bitsequence length being L.

A similar operation may be applied to a “puncturing from bottom ofcircular buffer with bit reversal” scheme. In such a scheme, bits may besaved to a circular buffer after bit reversal operations.

In an example where a repeat from top of circular buffer scheme may beapplied, where a repetition vector may be (1, . . . , 1, 0, . . . , 0),and where the first L bits are 1's and the last N−L bits are 0's, a pairof parameters (e.g., 1, N+L) may be determined. An exemplary bitselection is illustrated FIG. 10 . As illustrated in FIG. 10 , bits tobe used may start from a first position of a circular buffer, with thebit sequence length being N+L.

In an example where a repeat from bottom of circular buffer scheme maybe applied, where a repetition vector may be (0, . . . , 0, 1, . . . ,1), and where the first N−L bits are 0's and the last L bits are 1's, apair of parameters (e.g., N−L, N+L) may be determined. An exemplary bitselection is illustrated in FIG. 11 . As illustrated in FIG. 11 , bitsto be used may start from the first position of a circular buffer, withthe bit sequence length being N+L.

A starting point and/or an ending point may be on a first or a lastencoded bit. In some examples, neither a starting point nor an endingpoint may be on a first or a last encoded bit. Where a mixture of apuncturing from the top and a puncturing from the bottom schemes may beused, a starting point and an ending point may be in the middle ofencoded bits. In an example, where 1-bit shortening with puncturing fromthe top may be used, a puncturing vector may be (0, . . . , 0, 1, . . ., 1, 0), where the first L bits are 0's and the following N−L−1 bits are1's and the last bit is 0. A pair of parameters (e.g., L+1, N−1) may bedetermined. An exemplary bit selection is illustrated FIG. 12 .

Advanced PC polar code with CA list selection may be provided. Forexample, a polar code that is a mixture of PC polar code with CRC-aidedlist selection capability may be provided. FIGS. 13 and 14 illustrateexemplary encoding and decoding of CA polar code respectively with along CRC scenario (e.g., as described herein). FIG. 13 illustrates anexemplary encoding for CA polar code with a long CRC. FIG. 14illustrates an exemplary decoding for CA polar code with a long CRC.

As illustrated in FIG. 13 , at an encoding side, long CRC bits (J+J′)may be appended to the information bits. J of the order of 16 bits maybe used as the CRC length, e.g., as specified for an LTE controlchannel. Other values of J may be used, e.g., as specified for othercommunication systems. The value J′ may depend on list size L in acyclic redundancy check (CRC) aided successive cancellation list(CA-SCL) decoder. In an example, J′=log₂ L. The K+(J+J′) bits may beencoded utilizing a basic polar code, and rate matching may be applied.

As illustrated in FIG. 14 , at the decoder side, the demodulated symbolsmay be sent to the CA-SCL decoder. The SCL decoder block may output alist of L candidate sequences to the CRC aided (CA)-list selectionblock. The CA-list selection block may feedback the selected sequencebased on the CRC check results and/or priority of the candidatesequences. In case the L candidate sequences fail CRC check (e.g., allthe L candidate sequences fail CRC check), a detection error may bedeclared.

(J+J′) bits may be used in the CRC aided list selection process, e.g.,the error correction process. The error detection check may follow fromthe error correction, as the selected sequence may have passed CRCcheck.

FIGS. 15 and 16 illustrate exemplary encoding and decoding of CA polarcode respectively with two separate CRCs scenario (e.g., as describedherein). FIG. 15 illustrates an exemplary encoding for CA polar codewith two separate CRCs. FIG. 16 illustrates an exemplary decoding for CApolar code with two separate CRCs.

As illustrated in FIG. 15 , at an encoding side, the J CRC bits may beappended to the K information bits. These CRC bits may be utilized forerror detection. An additional J′ CRC bits may be appended to theinformation bits with error detection CRCs. These J′ CRC bits may beutilized for error correction. As illustrated in FIG. 15 , the resulting(K+J+J′) bits may be encoded by a PC polar coder. Rate matching may beapplied on the polar encoded bits.

As illustrated in FIG. 16 , at the decoder side, the demodulated symbolsmay be sent to the CA-SCL decoder, where the SCL decoder block mayprovide a list of L candidate sequences to the CA-list selection block.The CA-list selection block may feedback the selected sequence to theSCL decoder. The CA-list selection block may select a sequence based onthe J′-bit CRC check results and/or priority of the candidate sequences.In case the L candidate sequences fail CRC check (e.g., all these Lcandidate sequences fail CRC check), a detection error may be declared,as indicated by the downward arrow in FIG. 16 . The decoded sequence orerror declaration may be passed to the CRC check block. The CRC checkblock may use J bits CRC for error detection. If the CRC check passes,the sequence may be sent to the output. Otherwise, an error may bedetected and/or decoding failure may be declared.

FIGS. 17 and 18 illustrate exemplary encoding and decoding of PC polarcode respectively with CRC (e.g., as described herein). FIG. 17illustrates an exemplary encoding using a PC polar encoder. FIG. 18illustrates an exemplary decoding for a PC polar code.

As illustrated in FIG. 17 , at the encoding side, the J CRC bits may beappended to the K information bits. These CRC bits may be utilized forerror detection. The (K+J) bits may be encoded using a PC polar code.The PC polar encoded bits may be rate matched. In PC polar code, severalfrozen bits may be selected as PC frozen bits. The PC frozen bits may beutilized for error correction, e.g., in the candidate sequenceselection.

As illustrated in FIG. 18 , at the decoder side, the demodulated symbolsmay be sent to the PC-SCL decoder, where the PC-SCL decoder block mayoutput a single sequence. This sequence may be passed to the CRC check.If the CRC check passes, the sequence may be sent to the output,otherwise an error may be detected and/or decoding failure may bedeclared.

A PC polar code is disclosed that may be a combination of PC polar codeand CRC-aided list selection capability. Such an encoding may be similarto an exemplary PC polar coding case, for example, as described inregard to FIG. 17 .

FIG. 19 illustrates an exemplary decoder for a PC polar code withCRC-aided list selection. As illustrated in FIG. 19 , at the decoderside, the demodulated symbols may be sent to the concatenated PC-SCLdecoder. The concatenated PC-SCL decoder block may include a modifiedPC-SCL decoder sub-block and a CRC aided list selection sub-block. Themodified PC SCL decoder may generate a list of L candidate sequences tothe CA list selection, e.g., instead of a single sequence (e.g., asillustrated in FIG. 18 ). Each of the L candidate sequences may pass theinternal PC check in the decoder. The modified PC SCL decoder may outputL candidate sequences, as SCL decoder, e.g., unlike the PC SCL decoderwhich may output a single codeword. These L candidate sequences may beassociated with one or more ranks. The candidate sequences may pass theCRC check, e.g., based on the J CRC bits. If a high rank sequence passesthe CRC check, the sequence may be identified as the decoded sequence.If no sequences pass the CRC check, a detection/decoding failure may bedeclared.

The selection of the polar code type may depend on one or more of thefollowing: a WTRU capability, WTRU category, or a WTRU configuration.For example, for WTRUs with high capabilities, the advanced PC polarcode may be utilized. For WTRUs with low capabilities, the basic polarcode may be utilized. The selection of polar codes may be determinedbased on a WTRU category. For example, for a WTRU category of 1, 2, 3may correspond to basic polar code, while WTRU category of 4, 5, 6 maycorrespond to advanced PC polar code. The performance of CA polar codeand PC polar code may depend on a list size utilized in SCL decoding. PCpolar code may outperform CA polar code at a larger list size, while CApolar code may outperform PC polar code at a smaller list size. Theselection of a polar code to be utilized may depend on the list size, aWTRU may support. This list size may be part of the WTRU capabilities.

Puncturing vector generation for shortening and/or puncturing may beprovided. A puncturing and/or a shortening scheme may be utilized toexclude some bits out of the output coded bits. There may be no impacton the code construction. A shortening scheme may puncture output codedbits, and may set the corresponding input bits to zero. These input bitsmay be included in the frozen bits set. These input bits may bedifferent from the other frozen bits that may be set to a pre-definedvalue (e.g., a non-zero value). Because some input bits are pre-set asfrozen bits due to shortening, the frozen bit set may need to beadjusted accordingly.

The corresponding input bits may depend on the inclusion of bit reversal(BR) operation in polar encoding. When the BR operation is included inpolar encoding (G_(N)=B_(N)F^(⊗n)), an input bit index corresponding toan output bit may be the BR of the output bit index. When the BRoperation is not included in polar encoding (G_(N)=F^(⊗n)), an input bitmay correspond to an output bit if they have the same index.

A difference between puncturing and shortening may be the way decodingis performed. When a log-likelihood ratio (LLR) value or probability foreach output bit is calculated from the received signal, an LLR value orprobability for each punctured (shortened) output bit may be defined.For puncturing scheme, the LLR value may be set to be log(1)=0, e.g., asit is equally likely that the punctured bit is 0 or 1. For shorteningscheme, the LLR value may be set to log(0)=−∞, e.g., which may implythat the punctured bits are equal to 0 (e.g., always equal to 0).

The puncturing scheme and shortening scheme may result in a puncturingvector to be used at the rate matching block, as illustrated in FIG. 5 .The puncturing scheme and/or shortening scheme may be provided that maygenerate a common puncturing vector for puncturing and/or shortening.

In an example, let there be M bits to be punctured or shortened from amother code with length N=2^(n). Let P(i) be the position of the i^(th)punctured bits, 0≤i<M. Let I_(s)(i) be the input bit positioncorresponding to the punctured bit P(i). In case of shortening, theI_(s)(i) bits may be shortened and set as frozen bits.

In an example, I_(s)(i) may be selected as

I_(s)(i) = N − 1 − i, ifi < N/4,${{I_{s}(i)} = {{\frac{3}{4} \times N} - 1 - \left\lfloor \frac{i - \frac{N}{4}}{2} \right\rfloor}},{{{{if}i} \geq {N/4{and}{{mod}\left( {\left( {i - \frac{N}{4}} \right),2} \right)}}} = 0},$${{I_{s}(i)} = {{\frac{1}{2} \times N} - 1 - \left\lfloor \frac{i - \frac{N}{4}}{2} \right\rfloor}},{{{{if}i} \geq {N/4{and}{{mod}\left( {\left( {i - \frac{N}{4}} \right),2} \right)}}} = 1},$where └x┘ may be the largest integer less than x·mod(a, b) is theremainder of a/b.

This puncturing/shortening may be expanded as

I_(s)(i) = N − 1 − i, ifi < N/2^(G),${{I_{s}(i)} = {N - 1 - {\frac{N}{2^{G}} \times 2^{g}} - \left\lfloor \frac{i - \frac{N}{2^{G}}}{G} \right\rfloor}},{{{{if}i} \geq {N/2^{G}{and}{{mod}\left( {\left( {i - \frac{N}{2^{G}}} \right),G} \right)}}} = {g.}}$

In an example, I_(s)(i) may be selected as

${{I_{s}(i)} = {N - 1 - \left\lfloor \frac{i}{G} \right\rfloor}},{{{if}{{mod}\left( {i,G} \right)}} = 0}$${{I_{s}(i)} = {N - 1 - {\frac{N}{2^{G}} \times 2^{g - 1}} - \left\lfloor \frac{i}{G} \right\rfloor}},{{if}{{mod}\left( {\left( {i,G} \right) = {g \neq 0}} \right.}}$

In an example, sub-block based puncturing may be utilized. For a mothercode length N, the N bits (e.g., N polar encoded bits) may bepartitioned (e.g., equally partitioned) into b sub-blocks. The bsub-blocks may be partitioned in a sequential manner. The number ofsub-blocks b may be assumed to be a power of 2. Each sub-block may have

$B = {\frac{N}{b}{{bits}.}}$The I_(s)(i) may be selected as follows:

$\begin{matrix}{{I_{s}(i)} = {N - 1 - {B \times {d_{1}\left\lbrack \left\lfloor \frac{i}{B} \right\rfloor \right\rbrack}} - {d_{2}\left\lbrack {{mod}\left( {i,B} \right)} \right\rbrack}}} & (1)\end{matrix}$where the functions d₁ and d₂ may be independently pre-defined, or d₁may be a function of d₂. The function d₁( ) is a mapping function thatmay determine the location of the sub-blocks within the set ofsub-blocks. The function d₂ ( ) is a mapping function that may determinethe location of the bits within the sub-block.

In an example, d₂( ) may be defined in a way where d₂ [i]=i. d₁ maydepend on the reliability distributions of bit channels of polar codes.d₁[0] may correspond to the least reliable block of bit channels, d₁[1]may correspond to the second least reliable block of bit channels, andso on. For example, for the case of b=2, we have d₁[0]=0, d₁[1]=1; forthe case of b=4, we have d₁[0]=0, d₁[1]=1; d₁[2]=2, d₁[1]=3; for thecase of b=8, we haved ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=4, d ₁[4]=3, d ₁[5]=5, d ₁[6]=6, d₁[7]=7;  (Pattern 1)ord ₁[0]=0, d ₁[1]=1, d ₁[2]=4, d ₁[3]=2, d ₁[4]=3, d ₁[5]=5, d ₁[6]=6, d₁[7]=7Pattern 1 may be considered as

$\frac{b}{4}\left( {= 2} \right)$interleaver pattern

${+ \frac{b}{2}}\left( {= 4} \right)$interlaced pattern

${+ \frac{b}{4}}\left( {= 2} \right)$symmetric interleaver pattern from the ending index when b=8. Theinterleaver pattern for

$b^{\prime} = {\frac{b}{4} = 2}$is d₁[0]=0, d₁[1]=1 and Pattern 1 may be generated. The Pattern 1 may beexpressed in a table format as indicated in Table 3. Other patterns mayalso be expressed in a table form.

TABLE 3 i d₁ (i) 0 0 1 1 2 2 3 4 4 3 5 5 6 6 7 7For the case of b=16, we haved ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=4, d ₁[4]=8, d ₁[5]=3, d ₁[6]=5, d₁[7]=6, d ₁[8]=9, d ₁[9]=10, d ₁[10]=12, d ₁[11]=7, d ₁[12]=11, d₁[13]=13, d ₁[14]=14, d ₁[15]=15;  (Pattern 2)ord ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=3, d ₁[4]=4, d ₁[5]=8, d ₁[6]=5, d₁[7]=6, d ₁[8]=9, d ₁[9]=10, d ₁[10]=12, d ₁[11]=7, d ₁[12]=11, d₁[13]=13, d ₁[14]=14, d ₁[15]=15;ord ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=4, d ₁[4]=3, d ₁[5]=8, d ₁[6]=5, d₁[7]=6, d ₁[8]=9, d ₁[9]=10, d ₁[10]=12, d ₁[11]=7, d ₁[12]=11, d₁[13]=13, d ₁[14]=14, d ₁[15]=15;The Pattern 2 could be expressed in a table format as given in Table 4.

TABLE 4 i d₁ (i) i d₁ (i) i d₁ (i) i d₁ (i) 0 0 4 8 8 9 12 11 1 1 5 3 910 13 13 2 2 6 5 10 12 14 14 3 4 7 6 11 7 15 15for the case of b=32, we haved ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=4, d ₁[4]=8, d ₁[5]=16, d ₁[6]=3, d₁[7]=5, d ₁[8]=6, d ₁[9]=9, d ₁[10]=10, d ₁[11]=17, d ₁[12]=12, d₁[13]=18, d ₁[14]=20, d ₁[15]=7, d ₁[16]=24, d ₁[17]=11, d ₁[18]=13, d₁[19]=19, d ₁[20]=14, d ₁[21]=21, d ₁[22]=22, d ₁[23]=25, d ₁[24]=26, d₁[25]=28, d ₁[26]=15, d ₁[27]=23, d ₁[28]=27, d ₁[29]=29, d ₁[30]=30, d₁[31]=31.

The expression (1) may also be expressed as:

$\begin{matrix}{{I_{s}(i)} = {{B \times {d_{1}^{\prime}\left\lbrack \left\lfloor \frac{i}{B} \right\rfloor \right\rbrack}} + {d_{2}^{\prime}\left\lbrack {{mod}\left( {i,B} \right)} \right\rbrack}}} & (2)\end{matrix}$where d₁′[i]=b−1−d₁[i], d₂′[i]=B−1−d₂[i], and/or where d₁′[i]=d₁[i],d₂′[i]=d₂[i]. In an example, d₁( ) may be represented as in pattern (1)or pattern (2) or other patterns as described herein. In an example, d₂() may be represented as d₂(i)=i.

The values of d₁[i] may be derived by sorting the value representing foreach block i. If i indicates a block of input bit index from B×(i−1) toB×(i−1)+B−1, the representative value may be an average or minimum ormaximum reliability value for that range. d₁[i] may be the index of thesub-block which has i-th representative value.

Some d₁[i′] and d₁[i″] (i′≠i″) in the derived d₁[i] may be exchanged,e.g., to improve the property of Hamming distance and error performancefor shortening and puncturing. A common total puncturing vector forpuncturing and/or shortening may be used and a determination ofshortening or puncturing may be based on specific criteria. Such acriterion may be a code rate, as described herein.

A common total puncturing vector may be divided into a puncturing partand a shortening part, where such a common puncturing vector may beshared between puncturing and shortening. In an example, shortening maybe used for P(i), i<p₀, and puncturing may be used for P(i), i≥p₀. p₀may be fixed or may be dependent on a code rate (or mother code rate) orp. p may be a total number of puncturing and shortening, and poi p. Whenshortening may be used, corresponding input bit positions I_(s)(i) maybe set to 0, where P(i)=BR(I_(s)(i), n) in case the BR operation isapplied on the polar encoder, or where P(i)=I_(s)(i) in case the BRoperation is not applied on the polar encoder. Here, BR(x, n) may be thebit reversal of the integer x, in terms of n bits; Depending on theindices of these zero valued input bits, the unfrozen bits in polarencoder may be rearranged; these zero valued input bits may be excludedin the selection of unfrozen bits.

FIG. 20 illustrates an exemplary BLER comparison between the proposedsub-block based puncturing and the shortening scheme. In the shorteningexample of N=512, K=126, P=182, CA-SCL decoding, with a list size of 8,and a CRC length of 16 is applied. The example is a case of the secondpattern or b=16. From the results, the exemplary scheme may have acoding gain of ˜0.35 dB at a BLER of 10⁻³.

When R(i) is a position of i-th repeated bits, R(1)=P(N−1−(i % N)). imay be larger than N−1 for repetition. i may be less than N−1 forpuncturing and/or shortening. Based on a common puncturing vector thatmay be used for puncturing and shortening, a repetition pattern may beconfigured. An interleaver, such as an interleaver as described herein,may be configured based on R(i) or P(i), and an i-th bit position(index) after interleaving may be an R(i)-th bit position (index) beforeinterleaving (e.g., where an index starts from zero).

An interleaver pattern d₁( ) or d₁′( ) may be determined as indicated inexpressions 1 or 2 and may be used for sub-block level interleaving.Referring to expressions 1 or 2,

${B \times {d_{1}\left( \frac{i}{B} \right)}} + {d_{2}\left( {{mod}\left( {i,B} \right)} \right)}$may be an index of a bit before applying sub-block based interleavingthat corresponds to the i-th bit after the sub-block wise interleavingis applied. In this expression, i may be an index of a bit afterinterleaving. The number of bits in a sub-block or the size of asub-block, B may be determined by

${B = \frac{N}{b}},$where N is a number or polar encoded bits (e.g., mother code length),and b is the number of sub-blocks.

$\left\lfloor \frac{i}{B} \right\rfloor$may be index of an interleaved sub-block including i-th bit afterinterleaving.

$d_{1}\left( \frac{i}{B} \right)$may be index of a sub-block before interleaving. mod(i, B) may be indexof a i-th bit within an interleaved sub-block. d₂( ) may be interleaverpattern within a sub-block. In an example, an expression d₂(x)=x mayrepresent that no interleaving is applied within a sub-block. d₂(mod(i,B)) may be an index of a bit within a sub-block before interleaving thatcorresponds to the i-th bit within a sub-block after applying thesub-block level interleaving.

FIG. 21 illustrates an example of a sub-block interleaver with 8sub-blocks using

${B \times {d_{1}\left( \frac{i}{B} \right)}} + {d_{2}\left( {{mod}\left( {i,B} \right)} \right)}$index. In this example, the polar coded bits may be partitioned (e.g.,evenly and sequentially partitioned) to 8 sub-blocks (Subblock 0 toSubblock 7). These 8 sub-blocks may be interleaved based on aninterleaver pattern Pattern 1. Based on Pattern 1, these sub-blocks maybe re-arranged in the order of [0, 1, 2, 4, 3, 5, 6, 7]. The re-arrangedsub-blocks may be saved to circular buffer.

FIG. 22 illustrates an example of a sub-block interleaver with 16sub-blocks using

${B \times {d_{1}\left( \frac{i}{B} \right)}} + {d_{2}\left( {{mod}\left( {i,B} \right)} \right)}$index. The polar coded bits may be partitioned (e.g., evenlypartitioned) to 16 sub-blocks. These 16 sub-blocks may be interleavedbased on the interleaver pattern, Pattern 2, as described herein. Basedon Pattern 2, these sub-blocks may be re-arranged in the order of [0, 1,2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 15].

The interleaver pattern Pattern 1 may be extended to 16 sub-blocks, bydoubling each sub-block to two sub-blocks. For example, the middle 8sub-blocks may be interleaved or interlaced while the top 4 sub-blocksand the bottom 4 sub-blocks may remain unchanged. The interleaverpattern may be as follows:d ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=3, d ₁[4]=4, d ₁[5]=8, d ₁[6]=5, d₁[7]=9, d ₁[8]=6,d ₁[9]=10,d ₁[10]=7,d ₁[11]=11, d ₁[12]=12,d ₁[13]=13,d ₁[14]=14, d ₁[15]=15.

The interleaver pattern Pattern 1 as described herein could be extendedto 32 sub-blocks, by four times each sub-block. For example, the middle16 sub-blocks may be interlaced while the top 8 sub-blocks and thebottom 8 sub-blocks may remain unchanged. The interleaver pattern may beas follows:d ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=3, d ₁[4]=4, d ₁[5]=5, d ₁[6]=6, d₁[7]=7, d ₁[8]=8, d ₁[9]=16, d ₁[10]=9, d ₁[11]=17, d ₁[12]=10, d₁[13]=18, d ₁[14]=11, d ₁[15]=19, d ₁[16]=12, d ₁[17]=20, d ₁[18]=13, d₁[19]=21, d ₁[20]=14, d ₁[21]=22, d ₁[22]=15, d ₁[23]=23, d ₁[24]=24, d₁[25]=25, d ₁[26]=26, d ₁[27]=27, d ₁[28]=28, d ₁[29]=29, d ₁[30]=30, d₁[31]=31.

FIGS. 23A-23C illustrate an example of a sub-block interleaver with 32sub-blocks using B×d₁(i/B)+d₂(mod(i, B)) index. In this example, themiddle 16 sub-blocks may be interlaced while the top 8 sub-blocks andthe bottom 8 sub-blocks may be directly copied from the interleaverpattern Pattern 1, as described herein. This provides the interleaverpattern, Pattern 3 as follows:d ₁[0]=0, d ₁[1]=1, d ₁[2]=2, d ₁[3]=4, d ₁[4]=3, d ₁[5]=5, d ₁[6]=6, d₁[7]=7, d ₁[8]=8, d ₁[9]=16, d ₁[10]=9, d ₁[11]=17, d ₁[12]=10, d₁[13]=18, d ₁[14]=11, d ₁[15]=19, d ₁[16]=12, d ₁[17]=20, d ₁[18]=13, d₁[19]=21, d ₁[20]=14, d ₁[21]=22, d ₁[22]=15, d ₁[23]=23, d ₁[24]=24, d₁[25]=25, d ₁[26]=26, d ₁[27]=28, d ₁[28]=27, d ₁[29]=29, d ₁[30]=30, d₁[31]=31.  (Pattern 3)The Pattern 3 may be expressed in a table format as indicated in Table5.

TABLE 5 i d₁ (i) i d₁ (i) i d₁ (i) i d₁ (i) i d₁ (i) i d₁ (i) i d₁ (i) id₁ (i) 0 0 4 3 8 8 12 10 16 12 20 14 24 24 28 27 1 1 5 5 9 16 13 18 1720 21 22 25 25 29 29 2 2 6 6 10 9 14 11 18 13 22 15 26 26 30 30 3 4 7 711 17 15 19 19 21 23 23 27 28 31 31

Use of an interleaver after rate matching may be provided. A group basechannel interleaver may be provided. Output coded bits generated by apolar encoder may be interleaved. For example, the coded bits may beinterleaved after application of a rate matching function and/or beforemodulation. An exemplary interleaving operation may provide improvedblock error ratio (BLER) performance, for example, where high ordermodulation may be in use or fading channels may be present.

Input information bits may correspond to output coded bits. Inputinformation bits may have an associated reliability order. Rate matchedoutput coded bits may be ordered based on such a reliability orderassociated with respective corresponding input information bits.

c(i) may be a value of i-th encoded and rate matched bits, where i=0, 1,. . . , N−M may indicate bit indexes of output coded bits (e.g., naturalorder, serial indexing from a starting point). M may be a rate matchingparameter that may be a number of bits punctured or shortened. In anexample, rate matching may be performed by repetition. In such examples,M may be negative. When output bits are repeated, an index order of suchoutput bits may be associated with a same index order as that associatedwith the original repeated bits.

cr(j) may be a value of (N−M−1−j)-th reliable output coded bits and j=0,1, . . . , N−M may indicate a reliability index of output coded bits.The reliability order of output coded bits may follow a reliabilityorder of corresponding input bits. When corresponding input bits may befrozen bits and/or parity bits, an associated reliability order may be arelatively low and/or a lowest reliability order. When output bits maybe repeated, an associated reliability order may be a same reliabilityorder as that associated with original repeated bits.

In an example, Q=2^(q)-ary modulation may be used. A number of inputbits provided for modulation may be q. Such bits may be used to generatea modulation symbol. There may be a difference in reliability among suchq bits. For example, if q=4, first two bits may be classified as morereliable than the last two bits in LTE 16QAM. Two levels of reliabilitymay be provided for bits that are modulated using 16QAM.

In an example of using 64QAM (e.g., where q=6), bits may be classifiedinto three levels of reliability. First two bits may be classified asmost reliable, the next or second two bits may be classified as havinglower reliability than the first two bits, and the last two bits may beclassified as having the least reliability. 2^(q)-ary modulation mayhave q/2 levels of reliability. A number and quality of levels ofreliability may be utilized.

In an example, c(i), i=0, . . . , N−M bits may be divided into q/2blocks. The M bits may be evenly divided. BL(k) may indicate a k-thblock. After division, each block may be interleaved. An interleaver maybe a random interleaver, a block interleaver, a bit reversalinterleaver, a split natural interleaver, etc. The effect of aninterleaver selected used in rate matching may be counted (see, e.g.,FIG. 7 and accompanying description as provided herein). In an exampleutilizing a random interleaver, an interleaving pattern may be generatedfrom a pseudo-random sequence that may include, e.g., a gold sequence asfor example used in LTE technologies. In case of a block interleaver,the same or different interleaver depths may be applied to a blockinterleaver.

In an example, cr(j), j=0, . . . , N−M bits may be divided into q/2blocks. For example, the bits may be divided evenly. Each such block maybe indicated by BL(k). Each block, e.g., after division, may beinterleaved using one or more interleavers. Each BL(k) block, e.g.,after interleaving, may be mapped to input bits to be provided formodulation that may be associated with a specific reliability level.

Interleaved bits, for example, from the q/2 blocks described herein, maybe mapped to modulation symbols. In an example, bits with highreliability provided for modulation may be associated with rate matchedcoded bits with high reliability (e.g., that may correspond to the inputbits with high reliability). In an example, bits with low reliabilityprovided for modulation may be associated with rate matched coded bitswith low reliability (e.g., that may correspond to the input bits withlow reliability). A k-th component bit of a modulation symbol may beassociated with BL(k). FIG. 24 illustrates an exemplary implementationof such an example using 16QAM, where shaded boxes may indicate morereliable bits and unshaded boxes may indicate less reliable bits.

In an example, relatively less reliable bits provided for modulation maybe associated with relatively more reliable rate matched coded bits(e.g., the bits that may correspond to more reliable input bits). In anexample, relatively more reliable bits provided for modulation may beassociated with relatively less reliable input bits (e.g., the bits thatmay correspond to less reliable input bits). A k-th component bit of amodulation symbol may be associated with BL (q/2−k/2). FIG. 25illustrates an exemplary implementation of such an example using 16QAM,where shaded boxes may indicate more reliable bits and unshaded boxesmay indicate less reliable bits. These representations may apply to oneor more of encoded bits and component bits of a modulation symbolexamples. In other examples 64QAM modulation and/or 256QAM modulationmay be used.

In an example, coded and rate matched bits may be partitioned into q/2blocks. In an example, coded and rate matched bits may be partitionedinto q blocks. FIG. 26 illustrates an implementation of such an exampleusing 16QAM modulation and four partitions. As illustrated in FIG. 26 ,the shaded boxes may indicate more reliable bits and unshaded boxes mayindicate less reliable bits. FIG. 27 illustrates an example QPSKmodulation with two partitions. FIG. 28 illustrates an example QPSKmodulation with two partitions. A number of partitions for 2^(q)-arymodulation may comprise a number of partitions, e.g., (q−1) partitions,or prime number of partitions, etc. FIG. 29 illustrates an example QPSKmodulation with five partitions. The coded and rate matched bits may ormay not be partitioned evenly. For example, the blocks may havedifferent numbers of bits.

FIG. 30 illustrates an exemplary channel interleaver for physicalchannels. Using this parallel block interleaver operations may beapplied to uplink and/or downlink. Suppose the output of the ratematching may include M bits u₁, . . . , u_(M). These bits may bepartitioned to several groups. The number of groups may be denoted by p.For simplicity, M may be dividable by p. If M is not dividable by p,NULL bits or dummy bits may be inserted into the output of the ratematching such that the total number of bits is dividable by p.

The bits may be grouped based on sequential order. The first group mayinclude u₁, u₂, . . . , u_(M/p), the second group may include

$u_{\frac{M}{p} + 1},u_{\frac{M}{p} + 2},\ldots,u_{\frac{2M}{p}},\ldots,$and the p-th group may include

$u_{M - \frac{M}{p} + 1},\ldots,{u_{M}.}$The bits may be grouped based on interlacing order. The first group mayinclude u₁, u_(p+1), . . . , u_(M-p+1), the second group may include u₂,u_(p+2), . . . , u_(M-p+2), . . . , and the p-th group may includeu_(p), u_(2p), . . . , u_(M). The bits may be grouped based onsubgroup-wise operation. The subgroups v₁, . . . , v_(q) may begenerated, where a subgroup may include several bits from u₁, . . . ,u_(M). Subgroups v₁, . . . , v_(q) may be treated as the bits u₁, . . ., u_(M) in the operations described herein.

The grouped bits may be passed to its corresponding interleaver. Theinterleavers may be block interleavers the same depth, or could be blockinterleavers with different depths, or could be any interleaver. In anexample of a block interleaver, assuming d₁, d₂, . . . , d_(p) to be thedepth of these p block interleavers, some or all of d_(i) may havedifferent values. The depth value d_(i) may be a prime number. Othervalues of d_(i) may be possible.

The interleaved bits from p groups may be combined into a joint output.The grouped interleaved bits may be combined in a group sequentialorder. For example, the first group interleaved bits may be generatedfirst, the second group interleaved bits may be generated second, etc.The grouped interleaved bits may be combined in group order with acertain pattern. For example, the second group interleaved bits may begenerated first, the 5-th group interleaved bits may be generatedsecond, etc. The grouped interleaved bits may be combined in interlacingorder. For example, the order may be: the first bit from the firstgroup, the first bit from the second group, . . . , the first bit fromthe last group, the second bit from the first group, the second bit fromthe second group, . . . , the second bit from the last group, the thirdbit from the first group, . . . . The grouped interleaved bits may becombined in interlacing order jointly, for example, using a group order.

FIG. 31 illustrates an exemplary interleaving that may be performedbetween rate matching and modulation. In an example, interleaving may befirst be performed within a rate matching block. Interleaving performedafter a rate matching block may take into account interleaving performedas part of a rate matching block or function.

An example interleaver design may depend on a modulation order. Arow-column or block interleaver performing interleaving after a ratematching block or function for high order modulation and performance ina fading channel may be such that a number of rows may be equal to amodulation order or equal to a modulation order minus one.

The block interleaver after the rate matching block may be described bythe depth of the rate matching block. FIG. 32 illustrates an example ofa block interleaver with a depth of 5 (e.g., the number of rows of theblock interleaver). The depth of the block interleaver may depend on themodulation order. For example, for a 64QAM modulation, a blockinterleaver with a depth 7 may not be adequate (e.g., may not render adesired performance). For a 16QAM modulation, a block interleaver with adepth of 7 may be adequate (e.g., may render a desired performance).

As is illustrated in FIG. 33 . FIG. 34 , and FIG. 35 , a blockinterleaver with a depth of 11 may be adequate in a QPSK, 16QAM, and/or64QAM modulation orders, and in an AWGN channel and/or fading channel. Adepth of 11 block interleaver may follow FIG. 32 with the number of rowsequal to 11. A unified block interleaver with a fixed depth may be usedfor each of the supported modulation orders. For example, a unifiedblock interleaver with a fixed depth may be used for each of thesupported modulation orders for simplicity. Each of the supportedmodulations and/or modulation orders may include modulations and/ormodulation orders where a gain may be achieved by using the blockinterleaver. The block interleaver used may include a block interleaverwith a depth of 11 as the bit channel interleaver after the ratematching block for modulations, such as QPSK, 16QAM, 64QAM, 16QAM,and/or 64QAM. An example may use a block interleaver with a depth of 11as the bit channel interleaver after the rate matching block for each ofthe supported modulation orders, for example, for modulations that maybe higher than 64QAM. A triangle interleaver may be used after the ratematching block, for example, to achieve a performance like that achievedby a block interleaver. A random interleaver may be used after the ratematching block to achieve a performance like that achieved by a blockinterleaver and/or a triangle interleaver.

A block interleaver with different depths may be used. For example,different depths based on a modulation order may be used. For example, ablock interleaver with a depth of 5, a depth of 7, and/or a depth of 11may be applied to a QPSK modulation, and/or a block interleaver with adepth of 7 and/or a depth of 11 may be applied to a 16QAM modulation. Ablock interleaver with a depth of 5 and/or a depth of 11 may be appliedto a 64QAM modulation. A block interleaver with a depth of 11 may beapplied to a 16QAM modulation, and/or a block interleaver with a depthof 5 may be applied to a 64QAM modulation.

A depth of a block interleaver may be selected and/or specified based ona code rate. For example, at a high code rate, a smaller depth may beused. At a low code rate, a larger depth may be used. In an example of ½code rate one or more depths may be used to achieve similar block errorrate performance. In an example, a depth of 3 may be used for modulationorders (e.g., all modulation orders). In an example, with a code rate of⅙, a large depth (e.g., 11) may be used for better block error rateperformance than a shorter depth (e.g., 3 or 5). In an example, a depthof a block interleaver may be selected and/or specified based on amodulation order and/or a code rate, as described herein.

If a split-natural shortening or puncturing scheme is used as a ratematching scheme, an interleaver in a rate matching block or function maybe designed such that coded bits may be equally portioned to fourgroups. A second and third groups of the four groups may be interlaced.

FIG. 36 illustrates exemplary performance gain that may result from useof a row-column interleaver after a rate matching block for 16QAMmodulation. Performance simulations of a split-natural puncturingexample, a split-natural shortening example, a bit-reversal shorteningexample, and a natural repetition example may provide results asdescribed herein. In such simulations, QPSK modulation and AWGN channelmay be assumed. In such simulations, a polar code with PW sequence and aCA-SCL (L=8) decoding algorithm may be used. A 19-bit CRC may beappended to source data. Such CRC bits may be considered as part of theinformation bits.

Triangular channel interleaver may be used in an uplink (UL)transmission. Parallel rectangular interleaver may be used in a downlink(DL) transmission. A triangular channel interleaver may be provided.

In an example, let u₁, . . . , u_(M) be the M output bits of the ratematcher that may be transmitted. A minimum integer P may be determinedsuch that

$\frac{P\left( {P + 1} \right)}{2} \geq {M.}$Assuming

${Q = \frac{P\left( {P + 1} \right)}{2}},$and y₁, . . . , y_(Q) be y_(i)=u_(i), 1≤i≤M, and y_(i)=NULL, M+1≤i≤Q, abit sequence y₁, . . . , y_(Q) may be written to isosceles righttriangle row-by-row starting from the left upper corner of the array, asillustrated in FIG. 49 . The output of the triangular interleaver may bea bit sequence read out column by column starting from the first column,e.g., y₁, y_(P+1), y_(2P), . . . . In the process, the NULL bits may beskipped.

Various variations of the triangular interleaver may be provided. In anexample, NULL bits may be inserted the beginning of the bit sequencefrom the rate matching block. A minimum integer P may be determined suchthat

$\frac{P\left( {P + 1} \right)}{2} \geq {M.}$Assuming

${Q = \frac{P\left( {P + 1} \right)}{2}},$and y₁, . . . , y_(Q) be y_(i)=NULL, 1≤i≤Q−M, and y_(i)=u_(i-(Q-M)),Q−M+1≤i≤Q, the bit sequence y₁, . . . , y_(Q), may be written toisosceles right triangle row-by-row starting from the left upper cornerof the array. Column-wise permutation may be applied, for example. Theoutput of the triangular interleaver may be the bit sequence read outcolumn by column starting from the first column, e.g., y₁, y_(P+1),y_(2P), . . . . In the process, the NULL bits may be skipped. Insertingthe NULL bits at the beginning of bit sequence u₁, . . . , u_(M) may beavoided in order the first output bit to be u₁.

In an example, the right bottom corner of the array may be applied, asillustrated in FIG. 50 . The NULL bits may be inserted at the end of bitsequence u₁, . . . , u_(M). A minimum integer P may be determined suchthat

$\frac{P\left( {P + 1} \right)}{2} \geq {M.}$Assuming

${Q = \frac{P\left( {P + 1} \right)}{2}},$and y₁, . . . , y_(Q), be y_(i)=u_(i), 1≤i≤M, and let y_(i)=NULL,M+1≤i≤Q, the bit sequence, y₁, . . . , y_(Q) may be written to isoscelesright triangle row-by-row starting from the right bottom corner of thearray, as shown in in FIG. 50 . Column-wise permutation may be applied,for example. The output of the triangular interleaver may be the bitsequence read out column by column starting from the first column, e.g.,y_(Q-P+1), y_(Q-P+2), y_(Q-2P+2), . . . . In the process, the NULL bitsmay be skipped.

In an example, the right bottom corner of the array and the NULL bitsmay be inserted at the beginning of bit sequence u₁, . . . , u_(M). Aminimum integer P may be determined such that

$\frac{P\left( {P + 1} \right)}{2} \geq {M.}$Assuming

${Q = \frac{P\left( {P + 1} \right)}{2}},$and y₁, . . . , y_(Q), be y_(i)=NULL, 1≤i≤Q−M, and lety_(i)=u_(i-(Q-M)), Q−M+1≤i≤Q, the bit sequence y₁, . . . , y_(Q) may bewritten to isosceles right triangle row-by-row starting from the rightbottom corner of the array, as shown in in FIG. 50 . Column-wisepermutation may be applied, for example. The output of the triangularinterleaver may be the bit sequence read out column by column startingfrom the first column, e.g., y_(Q-P+1), y_(Q-P+2), y_(Q-2P+2) . . . . Inthe process, the NULL bits may be skipped. Column wise permutation maybe applied, for example to further randomize the output of thetriangular interleaver.

Parallel triangular interleaver may be applied as described herein. Forexample, M number of output bits from a rate matcher may be divided intoB groups. Each group may or may not have the same number of bits.Dummy/NULL bit(s) may be added to make each group have the same numberof bits. The number of groups may depend on modulation order. Differentways of partition of the M output bits of the rate matcher may beutilized. The triangular interleaver may be applied on the groups. Theoutput of the triangular interleaver for each group may be combined, forexample, via concatenation or interlacing operations. For example, letbe the output bits from the i-th group. Assuming that there are 4groups, the final output of the channel interleaver may be given byv_(1,1), v_(2,1), v_(3,1), v_(4,1), v_(1,2), v_(2,2), v_(3,2), v_(4,2),v_(1,3), . . . , v_(1,Q), v_(2,Q), v_(3,Q), v_(4,Q), if the interlacingoperation is applied. The example as illustrated in FIG. 30 may beapplied to triangular interleaver.

FIG. 51 illustrates an example of a polar encoding system. Asillustrated in FIG. 51 an exemplary polar encoding system may includeone or more of a CRC attachment and code construction block, a ratematching control block, a polar encoding block, a rate matching block, achannel interleaving block, or a modulation block. The channelinterleaving block may be referred as a channel interleaver or a bitinterleaver. In an example, the channel interleaving block may be partof the rate matching block. As illustrated in FIG. 51 , polar encodedbits N coming out of the polar encoding block may be rate matched basedon a rate matching scheme generated by the rate matching control block,as described herein. The rate matched bits M may be passed through thechannel interleaving block for interleaving M bits, as described herein.The bits after the channel interleaving block may be sent to themodulation block to generate modulation symbols, as described herein.

Although features and elements of the present disclosure may bedescribed in particular combinations, features or elements may be usedalone without other features and elements of the description or invarious combinations with or without other features and elements.Although the features described herein may consider New Radio (NR), 3G,4G, 5G, LTE, LTE-A, and/or other examples, it is understood that thefeatures described herein are not restricted to these technologies andmay be applicable to other wireless systems as well.

The processes described above may be implemented in a computer program,software, and/or firmware incorporated in a computer-readable medium forexecution by a computer and/or processor. Examples of computer-readablemedia include, but are not limited to, electronic signals (transmittedover wired and/or wireless connections) and/or computer-readable storagemedia. Examples of computer-readable storage media include, but are notlimited to, a read only memory (ROM), a random-access memory (RAM), aregister, cache memory, semiconductor memory devices, magnetic mediasuch as, but not limited to, internal hard disks and removable disks,magneto-optical media, and/or optical media such as CD-ROM disks, and/ordigital versatile disks (DVDs). A processor in association with softwaremay be used to implement a radio frequency transceiver for use in aWTRU, terminal, base station, RNC, and/or any host computer.

What is claimed is:
 1. A method implemented by a wirelesstransmit/receive unit (WTRU), the method comprising: generating aplurality of uplink control information (UCI) bits to be transmitted ina codeword; applying a polar code to the UCI bits, wherein a mother codelength associated with the polar code is determined based on a codewordlength for transmission of the UCI; performing rate matching on thepolar coded UCI bits, wherein performing the rate matching comprisesperforming one of: a repetition scheme if the mother code length is lessthan the codeword length, a puncturing scheme if a code rate for thecodeword is less than a threshold, or a shortening scheme if the coderate for the codeword is greater than the threshold; and transmittingthe rate matched, polar coded UCI bits.
 2. The method of claim 1,wherein the mother code length is determined based on the code rate. 3.The method of claim 1, wherein the codeword further includes a pluralityof cyclic redundancy check (CRC) bits.
 4. The method of claim 1, whereinthe code rate corresponds to a number of UCI bits and cyclic redundancycheck (CRC) bits in the codeword divided by a number of coded bits inthe codeword.
 5. The method of claim 1, wherein the puncturing scheme orthe shortening scheme is performed if the mother code length is greaterthan the codeword length.
 6. The method of claim 1, wherein performingthe rate matching further comprises: selecting the repetition scheme ifthe mother code length is less than the codeword length, or if therepetition scheme is not selected, selecting one of the puncturingscheme or the shortening scheme.
 7. The method of claim 1, wherein thepolar code comprises a concatenated polar code.
 8. The method of claim7, further comprising performing one of the repetition scheme, thepuncturing scheme, or the shortening scheme to the concatenated polarcode.
 9. A wireless transmit/receive unit (WTRU) comprising: atransceiver; and a processor configured to: generate a plurality ofuplink control information (UCI) bits to be transmitted in a codeword;apply a polar code to the UCI bits, wherein a mother code lengthassociated with the polar code is determined based on a codeword lengthfor transmission of the UCI; perform rate matching on the polar codedUCI bits, wherein the rate matching is performed using one of: arepetition scheme if the mother code length is less than the codewordlength, a puncturing scheme if a code rate for the codeword is less thana threshold, or a shortening scheme if the code rate for the codeword isgreater than the threshold; and transmit the rate matched, polar codedUCI bits.
 10. The WTRU of claim 9, wherein the mother code length isdetermined based on the code rate.
 11. The WTRU of claim 9, wherein thecodeword further includes a plurality of cyclic redundancy check (CRC)bits.
 12. The WTRU of claim 9, wherein the code rate corresponds to anumber of UCI bits and cyclic redundancy check (CRC) bits in thecodewords divided by a number of coded bits in the codeword.
 13. TheWTRU of claim 9, wherein the puncturing scheme or the shortening schemeis performed if the mother code length is greater than the codewordlength.
 14. The WTRU of claim 9, wherein the processor is furtherconfigured to perform rate matching by: selecting the repetition schemeif the mother code length is less than the codeword length, or if therepetition scheme is not selected, selecting one of the puncturingscheme or the shortening scheme.
 15. The WTRU of claim 9, wherein thepolar code comprises a concatenated polar code.
 16. The WTRU of claim15, wherein the processor is further configured to perform one of therepetition scheme, the puncturing scheme, or the shortening scheme tothe concatenated polar code.